diff --git a/src/account/accountMisc.js b/src/account/accountMisc.js
index 5f2252906ff..a246033bd43 100644
--- a/src/account/accountMisc.js
+++ b/src/account/accountMisc.js
@@ -10,7 +10,20 @@ export const identityOfAccount: Account => Identity = identitySlice;
 /** A string corresponding uniquely to an identity, for use in `Map`s. */
 export const keyOfIdentity = ({ realm, email }: Identity): string => `${realm}\0${email}`;
 
+const keyOfAuth = (auth: Auth): string => keyOfIdentity(identityOfAuth(auth));
+
 export const authOfAccount = (account: Account): Auth => {
   const { realm, email, apiKey } = account;
   return { realm, email, apiKey };
 };
+
+/**
+ * Takes two Auth objects and confirms that they are equal, either by
+ *  1.) strict equality
+ *  2.) equality of their identity key (realm + email) and API key
+ */
+export const authEquivalent = (auth1: Auth | void, auth2: Auth | void): boolean =>
+  auth1 === auth2
+  || (auth1 !== undefined
+    && auth2 !== undefined
+    && (auth1.apiKey === auth2.apiKey && keyOfAuth(auth1) === keyOfAuth(auth2)));
diff --git a/src/events/eventActions.js b/src/events/eventActions.js
index 09b4f49c345..a82200f61de 100644
--- a/src/events/eventActions.js
+++ b/src/events/eventActions.js
@@ -1,7 +1,7 @@
 /* @flow strict-local */
 import { batchActions } from 'redux-batched-actions';
 
-import type { Action, Dispatch, GeneralEvent, GetState, GlobalState } from '../types';
+import type { Auth, Action, Dispatch, GeneralEvent, GetState, GlobalState } from '../types';
 import * as api from '../api';
 import { logout } from '../account/accountActions';
 import { deadQueue } from '../session/sessionActions';
@@ -11,6 +11,7 @@ import { tryGetAuth } from '../selectors';
 import actionCreator from '../actionCreator';
 import { BackoffMachine } from '../utils/async';
 import { ApiError } from '../api/apiErrors';
+import { authEquivalent } from '../account/accountMisc';
 
 /** Convert an `/events` response into a sequence of our Redux actions. */
 export const responseToActions = (
@@ -44,12 +45,13 @@ export const dispatchOrBatch = (dispatch: Dispatch, actions: $ReadOnlyArray<Acti
 };
 
 /**
- * Poll an event queue on the Zulip server for updates, in a loop.
+ * Poll an event queue on the Zulip server for updates, in a loop, as long as
+ * the user remains logged into the same account.
  *
  * This is part of our use of the Zulip events system; see `doInitialFetch`
  * for discussion.
  */
-export const startEventPolling = (queueId: number, eventId: number) => async (
+export const startEventPolling = (auth: Auth, queueId: number, eventId: number) => async (
   dispatch: Dispatch,
   getState: GetState,
 ) => {
@@ -59,17 +61,19 @@ export const startEventPolling = (queueId: number, eventId: number) => async (
 
   // eslint-disable-next-line no-constant-condition
   while (true) {
-    const auth = tryGetAuth(getState());
-    if (!auth) {
-      // User switched accounts or logged out
+    if (!authEquivalent(auth, tryGetAuth(getState()))) {
+      // The user logged out or switched accounts during progressiveTimeout
+      // called from see catch block, below. (If tryGetAuth returns undefined,
+      // the user is not logged in.)
       break;
     }
 
     try {
       const { events } = await api.pollForEvents(auth, queueId, lastEventId);
 
-      // User switched accounts or logged out
-      if (queueId !== getState().session.eventQueueId) {
+      if (!authEquivalent(auth, tryGetAuth(getState()))) {
+        // The user logged out or switched accounts while api.pollForEvents was in progress.
+        // (If tryGetAuth returns undefined, the user is not logged in.)
         break;
       }
 
@@ -86,14 +90,14 @@ export const startEventPolling = (queueId: number, eventId: number) => async (
         break;
       }
 
-      // protection from inadvertent DDOS
-      await backoffMachine.wait();
-
       if (e instanceof ApiError && e.code === 'BAD_EVENT_QUEUE_ID') {
         // The event queue is too old or has been garbage collected.
         dispatch(deadQueue());
         break;
       }
+
+      // protection from inadvertent DOS
+      await backoffMachine.wait();
     }
   }
 };
diff --git a/src/message/fetchActions.js b/src/message/fetchActions.js
index d59c339a095..9f180b745d9 100644
--- a/src/message/fetchActions.js
+++ b/src/message/fetchActions.js
@@ -12,6 +12,7 @@ import type { InitialData } from '../api/initialDataTypes';
 import * as api from '../api';
 import {
   getAuth,
+  tryGetAuth,
   getSession,
   getFirstMessageId,
   getLastMessageId,
@@ -252,7 +253,19 @@ export const doInitialFetch = () => async (dispatch: Dispatch, getState: GetStat
   dispatch(realmInit(initData, serverSettings.zulip_version));
   dispatch(fetchTopMostNarrow());
   dispatch(initialFetchComplete());
-  dispatch(startEventPolling(initData.queue_id, initData.last_event_id));
+
+  const authNow = tryGetAuth(getState());
+  if (authNow !== undefined) {
+    // The user may have logged out while api.registerForEvents was in progress.
+    // If so, don't start polling events.
+
+    // TODO: If the user did log out during that time, other actions that are dispatched
+    // here (in doInitialFetch, after api.registerForEvents) will throw an error,
+    // which may be a cause of #3706! These include the calls to fetchTopMostNarrow,
+    // fetchPrivateMessages, and fetchMessagesInNarrow, because they all dispatch
+    // fetchMessages, which calls getAuth, which throws with 'Active account not logged in'.
+    dispatch(startEventPolling(authNow, initData.queue_id, initData.last_event_id));
+  }
 
   dispatch(fetchPrivateMessages());