diff --git a/spec/operators/shareReplay-spec.ts b/spec/operators/shareReplay-spec.ts
index 4b68b1c48b..52161ef120 100644
--- a/spec/operators/shareReplay-spec.ts
+++ b/spec/operators/shareReplay-spec.ts
@@ -2,7 +2,7 @@ import { expect } from 'chai';
 import * as sinon from 'sinon';
 import { shareReplay, mergeMapTo, retry, take } from 'rxjs/operators';
 import { TestScheduler } from 'rxjs/testing';
-import { Observable, Operator, Observer, of, from, defer, pipe } from 'rxjs';
+import { Observable, Operator, Observer, of, from, defer, pipe, combineLatest, firstValueFrom, BehaviorSubject } from 'rxjs';
 import { observableMatcher } from '../helpers/observableMatcher';
 
 /** @test {shareReplay} */
@@ -274,6 +274,20 @@ describe('shareReplay', () => {
     expect(subscriptions).to.equal(1);
   });
 
+  it('should only subscribe once each with multiple synchronous subscriptions and unsubscriptions ', async () => {
+    // This may seem very specific, but it's a regression test for https://github.com/ReactiveX/rxjs/issues/6760
+
+    let subscriptions = 0;
+    const source = defer(() => {
+      ++subscriptions;
+      // Needs to be an observable that doesn't complete
+      return new BehaviorSubject(1);
+    }).pipe(shareReplay({ bufferSize: 1, refCount: true }));
+
+    await firstValueFrom(combineLatest([source, source]));
+    expect(subscriptions).to.equal(1);
+  });
+
   it('should default to refCount being false', () => {
     testScheduler.run(({ cold, expectObservable, expectSubscriptions }) => {
       const source = cold('a-b-c-d-e-f-g-h-i-j');
diff --git a/src/internal/operators/share.ts b/src/internal/operators/share.ts
index 3c7facbc81..82c17f98f4 100644
--- a/src/internal/operators/share.ts
+++ b/src/internal/operators/share.ts
@@ -211,7 +211,13 @@ export function share<T>(options: ShareConfig<T> = {}): MonoTypeOperatorFunction
       // Basically, `subscriber === dest.subscribe(subscriber)` is `true`.
       dest.subscribe(subscriber);
 
-      if (!connection) {
+      if (
+        !connection &&
+        // Check this shareReplay is still activate - it can be reset to 0
+        // and be "unsubscribed" _before_ it actually subscribes.
+        // If we were to subscribe then, it'd leak and get stuck.
+        refCount > 0
+      ) {
         // We need to create a subscriber here - rather than pass an observer and
         // assign the returned subscription to connection - because it's possible
         // for reentrant subscriptions to the shared observable to occur and in