diff --git a/docs/src/index.md b/docs/src/index.md
index 9327acee..85c22213 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -1,4 +1,4 @@
-# Aqua.jl: 
+# Aqua.jl:
 ## *A*uto *QU*ality *A*ssurance for Julia packages
 
 Aqua.jl provides functions to run a few automatable checks for Julia packages:
@@ -13,6 +13,7 @@ Aqua.jl provides functions to run a few automatable checks for Julia packages:
   `compat` entry.
 * `Project.toml` formatting is compatible with Pkg.jl output.
 * There are no "obvious" type piracies.
+* The package does not create any persistent Tasks that might block precompilation of dependencies.
 
 ## Quick usage
 
@@ -55,14 +56,14 @@ recommended to add a version bound for Aqua.jl.
     test = ["Aqua", "Test"]
     ```
 
-If your package supports Julia pre-1.2, you need to use the second approach, 
+If your package supports Julia pre-1.2, you need to use the second approach,
 although you can use both approaches at the same time.
 
 !!! warning
     In normal use, `Aqua.jl` should not be added to `[deps]` in `YourPackage/Project.toml`!
 
 ### ...to your tests?
-It is recommended to create a separate file `YourPackage/test/Aqua.jl` that gets included in `YourPackage/test/runtests.jl` 
+It is recommended to create a separate file `YourPackage/test/Aqua.jl` that gets included in `YourPackage/test/runtests.jl`
 with either
 
 ```julia
diff --git a/src/Aqua.jl b/src/Aqua.jl
index 2f203016..98ba7b91 100644
--- a/src/Aqua.jl
+++ b/src/Aqua.jl
@@ -1,7 +1,7 @@
 module Aqua
 
 using Base: PkgId, UUID
-using Pkg: Pkg, TOML
+using Pkg: Pkg, TOML, PackageSpec
 using Test
 
 try
@@ -22,6 +22,7 @@ include("stale_deps.jl")
 include("deps_compat.jl")
 include("project_toml_formatting.jl")
 include("piracy.jl")
+include("persistent_tasks.jl")
 
 """
     test_all(testtarget::Module)
@@ -36,6 +37,7 @@ Run following tests in isolated testset:
 * [`test_deps_compat(testtarget)`](@ref test_deps_compat)
 * [`test_project_toml_formatting(testtarget)`](@ref test_project_toml_formatting)
 * [`test_piracy(testtarget)`](@ref test_piracy)
+* [`test_persistent_tasks(testtarget)`](@ref test_persistent_tasks)
 
 The keyword argument `\$x` (e.g., `ambiguities`) can be used to
 control whether or not to run `test_\$x` (e.g., `test_ambiguities`).
@@ -51,6 +53,7 @@ passed to `\$x` to specify the keyword arguments for `test_\$x`.
 - `deps_compat = true`
 - `project_toml_formatting = true`
 - `piracy = true`
+- `persistent_tasks = true`
 """
 function test_all(
     testtarget::Module;
@@ -62,6 +65,7 @@ function test_all(
     deps_compat = true,
     project_toml_formatting = true,
     piracy = true,
+    persistent_tasks = true,
 )
     @testset "Method ambiguity" begin
         if ambiguities !== false
@@ -103,6 +107,11 @@ function test_all(
             test_piracy(testtarget; askwargs(piracy)...)
         end
     end
+    @testset "Persistent tasks" begin
+        if persistent_tasks !== false
+            test_persistent_tasks(testtarget; askwargs(persistent_tasks)...)
+        end
+    end
 end
 
 end # module
diff --git a/src/persistent_tasks.jl b/src/persistent_tasks.jl
new file mode 100644
index 00000000..3e21caa4
--- /dev/null
+++ b/src/persistent_tasks.jl
@@ -0,0 +1,145 @@
+"""
+    Aqua.test_persistent_tasks(package; tmax=5)
+
+Test whether loading `package` creates persistent `Task`s
+which may block precompilation of dependent packages.
+
+# Motivation
+
+Julia 1.10 and higher wait for all running `Task`s to finish
+before writing out the precompiled (cached) version of the package.
+One consequence is that a package that launches
+`Task`s in its `__init__` function may precompile successfully,
+but block precompilation of any packages that depend on it.
+
+# Example
+
+Let's create a dummy package, `PkgA`, that launches a persistent `Task`:
+
+```julia
+
+```julia
+module PkgA
+const t = Ref{Any}()   # to prevent the Timer from being garbage-collected
+__init__() = t[] = Timer(0.1; interval=1)   # create a persistent `Timer` `Task`
+end
+```
+
+`PkgA` will precompile successfully, because `PkgA.__init__()` does not
+run when `PkgA` is precompiled. However,
+
+```julia
+module PkgB
+using PkgA
+end
+```
+
+fails to precompile: `using PkgA` runs `PkgA.__init__()`, which
+leaves the `Timer` `Task` running, and that causes precompilation
+of `PkgB` to hang.
+
+# How the test works
+
+This test works by launching a Julia process that tries to precompile a
+dummy package similar to `PkgB` above, modified to signal back to Aqua when
+`PkgA` has finished loading. The test fails if the gap between loading `PkgA`
+and finishing precompilation exceeds time `tmax`.
+
+# How to fix failing packages
+
+Often, the easiest fix is to modify the `__init__` function to check whether the
+Julia process is precompiling some other package; if so, don't launch the
+persistent `Task`s.
+
+```
+function __init__()
+    # Other setup code here
+    if ccall(:jl_generating_output, Cint, ()) == 0   # if we're not precompiling...
+        # launch persistent tasks here
+    end
+end
+```
+
+In more complex cases, you may need to set up independently-callable functions
+to launch the tasks and cleanly shut them down.
+
+# Arguments
+- `package`: a top-level `Module` or `Base.PkgId`.
+
+# Keyword Arguments
+- `tmax::Real`: the maximum time (in seconds) to wait between loading the
+  package and forced shutdown of the precompilation process.
+"""
+function test_persistent_tasks(package::PkgId; tmax=5, fails::Bool=false)
+    @testset "$package persistent_tasks" begin
+        result = root_project_or_failed_lazytest(package)
+        result isa LazyTestResult && return result
+        @test fails ⊻ precompile_wrapper(result, tmax)
+    end
+end
+
+function test_persistent_tasks(package::Module; kwargs...)
+    test_persistent_tasks(PkgId(package); kwargs...)
+end
+
+"""
+    Aqua.test_persistent_tasks_deps(package; kwargs...)
+
+Test all the dependencies of `package` with [`Aqua.test_persistent_tasks`](@ref).
+"""
+function test_persistent_tasks_deps(package::PkgId; fails=Dict{String,Bool}(), kwargs...)
+    result = root_project_or_failed_lazytest(package)
+    result isa LazyTestResult && return result
+    prj = TOML.parsefile(result)
+    deps = get(prj, "deps", nothing)
+    @testset "$result" begin
+        if deps === nothing
+            return LazyTestResult("$package", "`$result` does not have `deps`", true)
+        else
+            for (name, uuid) in deps
+                id = PkgId(UUID(uuid), name)
+                test_persistent_tasks(id; fails=get(fails, name, false), kwargs...)
+            end
+        end
+    end
+end
+
+function test_persistent_tasks_deps(package::Module; kwargs...)
+    test_persistent_tasks_deps(PkgId(package); kwargs...)
+end
+
+function precompile_wrapper(project, tmax)
+    pkgdir = dirname(project)
+    pkgname = basename(pkgdir)
+    wrapperdir = tempname()
+    wrappername, wrapperuuid = only(Pkg.generate(wrapperdir))
+    Pkg.activate(wrapperdir)
+    Pkg.develop(PackageSpec(path=pkgdir))
+    open(joinpath(wrapperdir, "src", wrappername * ".jl"), "w") do io
+        println(io, """
+        module $wrappername
+        using $pkgname
+        # Signal Aqua from the precompilation process that we've finished loading the package
+        open(joinpath("$wrapperdir", "done.log"), "w") do io
+            println(io, "done")
+        end
+        end
+        """)
+    end
+    # Precompile the wrapper package
+    cmd = `$(Base.julia_cmd()) --project=$wrapperdir -e 'using Pkg; Pkg.precompile()'`
+    proc = run(cmd; wait=false)
+    while !isfile(joinpath(wrapperdir, "done.log"))
+        sleep(0.1)
+    end
+    # Check whether precompilation finishes in the required time
+    t = time()
+    while process_running(proc) && time() - t < tmax
+        sleep(0.1)
+    end
+    success = !process_running(proc)
+    if !success
+        kill(proc)
+    end
+    return success
+end
diff --git a/test/pkgs/PersistentTasks/PersistentTask/Project.toml b/test/pkgs/PersistentTasks/PersistentTask/Project.toml
new file mode 100644
index 00000000..9f5cf185
--- /dev/null
+++ b/test/pkgs/PersistentTasks/PersistentTask/Project.toml
@@ -0,0 +1,4 @@
+name = "PersistentTask"
+uuid = "e5c298b6-d81d-47aa-a9ed-5ea983e22986"
+authors = ["Tim Holy <tim.holy@gmail.com>"]
+version = "0.1.0"
diff --git a/test/pkgs/PersistentTasks/PersistentTask/src/PersistentTask.jl b/test/pkgs/PersistentTasks/PersistentTask/src/PersistentTask.jl
new file mode 100644
index 00000000..5778f94a
--- /dev/null
+++ b/test/pkgs/PersistentTasks/PersistentTask/src/PersistentTask.jl
@@ -0,0 +1,6 @@
+module PersistentTask
+
+const t = Ref{Any}()
+__init__() = t[] = Timer(0.1; interval=1)   # create a persistent `Timer` `Task`
+
+end # module PersistentTask
diff --git a/test/pkgs/PersistentTasks/TransientTask/Project.toml b/test/pkgs/PersistentTasks/TransientTask/Project.toml
new file mode 100644
index 00000000..e69799be
--- /dev/null
+++ b/test/pkgs/PersistentTasks/TransientTask/Project.toml
@@ -0,0 +1,4 @@
+name = "TransientTask"
+uuid = "94ae9332-58b0-4342-989c-0a7e44abcca9"
+authors = ["Tim Holy <tim.holy@gmail.com>"]
+version = "0.1.0"
diff --git a/test/pkgs/PersistentTasks/TransientTask/src/TransientTask.jl b/test/pkgs/PersistentTasks/TransientTask/src/TransientTask.jl
new file mode 100644
index 00000000..7a8d09ec
--- /dev/null
+++ b/test/pkgs/PersistentTasks/TransientTask/src/TransientTask.jl
@@ -0,0 +1,5 @@
+module TransientTask
+
+__init__() = Timer(0.1)   # create a transient `Timer` `Task`
+
+end # module TransientTask
diff --git a/test/pkgs/PersistentTasks/UsesBoth/Project.toml b/test/pkgs/PersistentTasks/UsesBoth/Project.toml
new file mode 100644
index 00000000..98a85e9f
--- /dev/null
+++ b/test/pkgs/PersistentTasks/UsesBoth/Project.toml
@@ -0,0 +1,8 @@
+name = "UsesBoth"
+uuid = "96f12b6e-60f8-43dc-b131-049a88a2f499"
+authors = ["Tim Holy <tim.holy@gmail.com>"]
+version = "0.1.0"
+
+[deps]
+PersistentTask = "e5c298b6-d81d-47aa-a9ed-5ea983e22986"
+TransientTask = "94ae9332-58b0-4342-989c-0a7e44abcca9"
diff --git a/test/pkgs/PersistentTasks/UsesBoth/src/UsesBoth.jl b/test/pkgs/PersistentTasks/UsesBoth/src/UsesBoth.jl
new file mode 100644
index 00000000..7f45db8d
--- /dev/null
+++ b/test/pkgs/PersistentTasks/UsesBoth/src/UsesBoth.jl
@@ -0,0 +1,6 @@
+module UsesBoth
+
+using TransientTask
+using PersistentTask
+
+end # module UsesBoth
diff --git a/test/test_persistent_tasks.jl b/test/test_persistent_tasks.jl
new file mode 100644
index 00000000..7082ded9
--- /dev/null
+++ b/test/test_persistent_tasks.jl
@@ -0,0 +1,28 @@
+module TestPersistentTasks
+
+include("preamble.jl")
+using Base: PkgId, UUID
+using Pkg: TOML
+
+function getid(name)
+    path = joinpath(@__DIR__, "pkgs", "PersistentTasks", name)
+    if path ∉ LOAD_PATH
+        pushfirst!(LOAD_PATH, path)
+    end
+    prj = TOML.parsefile(joinpath(path, "Project.toml"))
+    return PkgId(UUID(prj["uuid"]), prj["name"])
+end
+
+
+@testset "PersistentTasks" begin
+    Aqua.test_persistent_tasks(getid("TransientTask"))
+    Aqua.test_persistent_tasks_deps(getid("TransientTask"))
+
+    if all((Base.VERSION.major, Base.VERSION.minor) .>= (1, 10))
+        Aqua.test_persistent_tasks(getid("PersistentTask"); fails=true)
+        Aqua.test_persistent_tasks_deps(getid("UsesBoth"); fails=Dict("PersistentTask" => true))
+    end
+    filter!(str -> !occursin("PersistentTasks", str), LOAD_PATH)
+end
+
+end