diff --git a/Sources/ObservableStore/ObservableStore.swift b/Sources/ObservableStore/ObservableStore.swift
index 8f561df..be6b197 100644
--- a/Sources/ObservableStore/ObservableStore.swift
+++ b/Sources/ObservableStore/ObservableStore.swift
@@ -204,8 +204,8 @@ public protocol StoreProtocol {
 public final class Store<Model>: ObservableObject, StoreProtocol
 where Model: ModelProtocol
 {
-    /// Cancellable for fx subscription.
-    private var cancelFx: AnyCancellable?
+    /// Stores cancellables by ID
+    private(set) var cancellables: [UUID: AnyCancellable] = [:]
     
     /// Private for all actions sent to the store.
     private var _actions = PassthroughSubject<Model.Action, Never>()
@@ -215,17 +215,6 @@ where Model: ModelProtocol
         _actions.eraseToAnyPublisher()
     }
     
-    /// Source publisher for batches of fx modeled as publishers.
-    private var _fxBatches = PassthroughSubject<Fx<Model.Action>, Never>()
-    
-    /// `fx` represents a flat stream of actions from all fx publishers.
-    private var fx: AnyPublisher<Model.Action, Never> {
-        _fxBatches
-            .flatMap({ publisher in publisher })
-            .receive(on: DispatchQueue.main)
-            .eraseToAnyPublisher()
-    }
-    
     /// Publisher for updates performed on state
     private var _updates = PassthroughSubject<Model.UpdateType, Never>()
 
@@ -273,11 +262,6 @@ where Model: ModelProtocol
             subsystem: "ObservableStore",
             category: "Store"
         )
-
-        self.cancelFx = self.fx
-            .sink(receiveValue: { [weak self] action in
-                self?.send(action)
-            })
     }
 
     /// Initialize with a closure that receives environment.
@@ -318,12 +302,49 @@ where Model: ModelProtocol
         self.send(action)
     }
 
-    /// Subscribe to a publisher of actions, send the actions it publishes
-    /// to the store.
+    /// Subscribe to a publisher of actions, piping them through to
+    /// the store.
+    ///
+    /// Holds on to the cancellable until publisher completes.
+    /// When publisher completes, removes cancellable.
     public func subscribe(to fx: Fx<Model.Action>) {
-        self._fxBatches.send(fx)
+        // Create a UUID for the cancellable.
+        // Store cancellable in dictionary by UUID.
+        // Remove cancellable from dictionary upon effect completion.
+        // This retains the effect pipeline for as long as it takes to complete
+        // the effect, and then removes it, so we don't have a cancellables
+        // memory leak.
+        let id = UUID()
+
+        // Receive Fx on main thread. This does two important things:
+        //
+        // First, SwiftUI requires that any state mutations that would change
+        // views happen on the main thread. Receiving on main ensures that
+        // all fx-driven state transitions happen on main, even if the
+        // publisher is off-main-thread.
+        //
+        // Second, if we didn't schedule receive on main, it would be possible
+        // for publishers to complete immediately, causing receiveCompletion
+        // to attempt to remove the publisher from `cancellables` before
+        // it is added. By scheduling to receive publisher on main,
+        // we force publisher to complete on next tick, ensuring that it
+        // is always first added, then removed from `cancellables`.
+        let cancellable = fx
+            .receive(
+                on: DispatchQueue.main,
+                options: .init(qos: .default)
+            )
+            .sink(
+                receiveCompletion: { [weak self] _ in
+                    self?.cancellables.removeValue(forKey: id)
+                },
+                receiveValue: { [weak self] action in
+                    self?.send(action)
+                }
+            )
+        self.cancellables[id] = cancellable
     }
-
+    
     /// Send an action to the store to update state and generate effects.
     /// Any effects generated are fed back into the store.
     ///
diff --git a/Tests/ObservableStoreTests/ObservableStoreTests.swift b/Tests/ObservableStoreTests/ObservableStoreTests.swift
index 1b7c492..fd164d6 100644
--- a/Tests/ObservableStoreTests/ObservableStoreTests.swift
+++ b/Tests/ObservableStoreTests/ObservableStoreTests.swift
@@ -97,6 +97,86 @@ final class ObservableStoreTests: XCTestCase {
         XCTAssertEqual(store.state.count, 1, "state is advanced")
     }
 
+    /// Tests that the immediately-completing empty Fx used as the default for
+    /// updates get removed from the cancellables array.
+    ///
+    /// Failure to remove immediately-completing fx would cause a memory leak.
+    func testEmptyFxRemovedOnComplete() {
+        let store = Store(
+            state: AppModel(),
+            environment: AppModel.Environment()
+        )
+        store.send(.increment)
+        store.send(.increment)
+        store.send(.increment)
+        let expectation = XCTestExpectation(
+            description: "cancellable removed when publisher completes"
+        )
+        DispatchQueue.main.async {
+            XCTAssertEqual(
+                store.cancellables.count,
+                0,
+                "cancellables removed when publisher completes"
+            )
+            expectation.fulfill()
+        }
+        wait(for: [expectation], timeout: 0.1)
+    }
+
+    /// Tests that immediately-completing Fx get removed from the cancellables.
+    ///
+    /// array. Failure to remove immediately-completing fx would cause a
+    /// memory leak.
+    ///
+    /// When you don't specify fx for an update, we default to
+    /// an immediately-completing `Empty` publisher, so this test is
+    /// technically the same as the one above. The difference is that it
+    /// does not rely on an implementation detail of `Update` but instead
+    /// tests this behavior directly, in case the implementation were to
+    /// change somehow.
+    func testEmptyFxThatCompleteImmiedatelyRemovedOnComplete() {
+        let store = Store(
+            state: AppModel(),
+            environment: AppModel.Environment()
+        )
+        store.send(.createEmptyFxThatCompletesImmediately)
+        store.send(.createEmptyFxThatCompletesImmediately)
+        store.send(.createEmptyFxThatCompletesImmediately)
+        let expectation = XCTestExpectation(
+            description: "cancellable removed when publisher completes"
+        )
+        DispatchQueue.main.async {
+            XCTAssertEqual(
+                store.cancellables.count,
+                0,
+                "cancellables removed when publisher completes"
+            )
+            expectation.fulfill()
+        }
+        wait(for: [expectation], timeout: 0.1)
+    }
+
+    func testAsyncFxRemovedOnComplete() {
+        let store = Store(
+            state: AppModel(),
+            environment: AppModel.Environment()
+        )
+        store.send(.delayIncrement(0.1))
+        store.send(.delayIncrement(0.2))
+        let expectation = XCTestExpectation(
+            description: "cancellable removed when publisher completes"
+        )
+        DispatchQueue.main.asyncAfter(deadline: .now() + 0.3) {
+            XCTAssertEqual(
+                store.cancellables.count,
+                0,
+                "cancellables removed when publisher completes"
+            )
+            expectation.fulfill()
+        }
+        wait(for: [expectation], timeout: 0.5)
+    }
+
     func testPublishedPropertyFires() throws {
         let store = Store(
             state: AppModel(),