diff --git a/src/Symfony/Component/HttpClient/Internal/ClientState.php b/src/Symfony/Component/HttpClient/Internal/ClientState.php
index c316e7b078920..52fe3c8c054c7 100644
--- a/src/Symfony/Component/HttpClient/Internal/ClientState.php
+++ b/src/Symfony/Component/HttpClient/Internal/ClientState.php
@@ -22,4 +22,5 @@ class ClientState
 {
     public $handlesActivity = [];
     public $openHandles = [];
+    public $lastTimeout;
 }
diff --git a/src/Symfony/Component/HttpClient/Response/ResponseTrait.php b/src/Symfony/Component/HttpClient/Response/ResponseTrait.php
index 69caabf4b85d0..0f041d4d02d21 100644
--- a/src/Symfony/Component/HttpClient/Response/ResponseTrait.php
+++ b/src/Symfony/Component/HttpClient/Response/ResponseTrait.php
@@ -233,15 +233,15 @@ abstract protected static function perform(ClientState $multi, array &$responses
      */
     abstract protected static function select(ClientState $multi, float $timeout): int;
 
-    private static function initialize(self $response): void
+    private static function initialize(self $response, float $timeout = null): void
     {
         if (null !== $response->info['error']) {
             throw new TransportException($response->info['error']);
         }
 
         try {
-            if (($response->initializer)($response)) {
-                foreach (self::stream([$response]) as $chunk) {
+            if (($response->initializer)($response, $timeout)) {
+                foreach (self::stream([$response], $timeout) as $chunk) {
                     if ($chunk->isFirst()) {
                         break;
                     }
@@ -304,7 +304,7 @@ private function doDestruct()
         $this->shouldBuffer = true;
 
         if ($this->initializer && null === $this->info['error']) {
-            self::initialize($this);
+            self::initialize($this, -0.0);
             $this->checkStatusCode();
         }
     }
@@ -325,6 +325,12 @@ public static function stream(iterable $responses, float $timeout = null): \Gene
         $lastActivity = microtime(true);
         $elapsedTimeout = 0;
 
+        if ($fromLastTimeout = 0.0 === $timeout && '-0' === (string) $timeout) {
+            $timeout = null;
+        } elseif ($fromLastTimeout = 0 > $timeout) {
+            $timeout = -$timeout;
+        }
+
         while (true) {
             $hasActivity = false;
             $timeoutMax = 0;
@@ -340,13 +346,18 @@ public static function stream(iterable $responses, float $timeout = null): \Gene
                     $timeoutMin = min($timeoutMin, $response->timeout, 1);
                     $chunk = false;
 
+                    if ($fromLastTimeout && null !== $multi->lastTimeout) {
+                        $elapsedTimeout = microtime(true) - $multi->lastTimeout;
+                    }
+
                     if (isset($multi->handlesActivity[$j])) {
-                        // no-op
+                        $multi->lastTimeout = null;
                     } elseif (!isset($multi->openHandles[$j])) {
                         unset($responses[$j]);
                         continue;
                     } elseif ($elapsedTimeout >= $timeoutMax) {
                         $multi->handlesActivity[$j] = [new ErrorChunk($response->offset, sprintf('Idle timeout reached for "%s".', $response->getInfo('url')))];
+                        $multi->lastTimeout ?? $multi->lastTimeout = $lastActivity;
                     } else {
                         continue;
                     }
diff --git a/src/Symfony/Component/HttpClient/Tests/HttpClientTestCase.php b/src/Symfony/Component/HttpClient/Tests/HttpClientTestCase.php
index a3782df49e5ed..85466d33b5438 100644
--- a/src/Symfony/Component/HttpClient/Tests/HttpClientTestCase.php
+++ b/src/Symfony/Component/HttpClient/Tests/HttpClientTestCase.php
@@ -19,6 +19,15 @@
 
 abstract class HttpClientTestCase extends BaseHttpClientTestCase
 {
+    public function testTimeoutOnDestruct()
+    {
+        if (!method_exists(parent::class, 'testTimeoutOnDestruct')) {
+            $this->markTestSkipped('BaseHttpClientTestCase doesn\'t have testTimeoutOnDestruct().');
+        }
+
+        parent::testTimeoutOnDestruct();
+    }
+
     public function testAcceptHeader()
     {
         $client = $this->getHttpClient(__FUNCTION__);
diff --git a/src/Symfony/Component/HttpClient/Tests/MockHttpClientTest.php b/src/Symfony/Component/HttpClient/Tests/MockHttpClientTest.php
index 27cc87f0ccfbd..75bf16d3e6c86 100644
--- a/src/Symfony/Component/HttpClient/Tests/MockHttpClientTest.php
+++ b/src/Symfony/Component/HttpClient/Tests/MockHttpClientTest.php
@@ -115,6 +115,10 @@ protected function getHttpClient(string $testCase): HttpClientInterface
                 $this->markTestSkipped('Real transport required');
                 break;
 
+            case 'testTimeoutOnDestruct':
+                $this->markTestSkipped('Real transport required');
+                break;
+
             case 'testDestruct':
                 $this->markTestSkipped("MockHttpClient doesn't timeout on destruct");
                 break;
diff --git a/src/Symfony/Component/HttpClient/Tests/NativeHttpClientTest.php b/src/Symfony/Component/HttpClient/Tests/NativeHttpClientTest.php
index bcfab64bdcace..2f76cc91c609f 100644
--- a/src/Symfony/Component/HttpClient/Tests/NativeHttpClientTest.php
+++ b/src/Symfony/Component/HttpClient/Tests/NativeHttpClientTest.php
@@ -25,4 +25,9 @@ public function testInformationalResponseStream()
     {
         $this->markTestSkipped('NativeHttpClient doesn\'t support informational status codes.');
     }
+
+    public function testTimeoutOnDestruct()
+    {
+        $this->markTestSkipped('NativeHttpClient doesn\'t support opening concurrent requests.');
+    }
 }
diff --git a/src/Symfony/Contracts/HttpClient/Test/HttpClientTestCase.php b/src/Symfony/Contracts/HttpClient/Test/HttpClientTestCase.php
index f3e75c9337c2c..1062c7c024b4d 100644
--- a/src/Symfony/Contracts/HttpClient/Test/HttpClientTestCase.php
+++ b/src/Symfony/Contracts/HttpClient/Test/HttpClientTestCase.php
@@ -810,6 +810,38 @@ public function testTimeoutWithActiveConcurrentStream()
         }
     }
 
+    public function testTimeoutOnDestruct()
+    {
+        $p1 = TestHttpServer::start(8067);
+        $p2 = TestHttpServer::start(8077);
+
+        $client = $this->getHttpClient(__FUNCTION__);
+        $start = microtime(true);
+        $responses = [];
+
+        $responses[] = $client->request('GET', 'http://localhost:8067/timeout-header', ['timeout' => 0.25]);
+        $responses[] = $client->request('GET', 'http://localhost:8077/timeout-header', ['timeout' => 0.25]);
+        $responses[] = $client->request('GET', 'http://localhost:8067/timeout-header', ['timeout' => 0.25]);
+        $responses[] = $client->request('GET', 'http://localhost:8077/timeout-header', ['timeout' => 0.25]);
+
+        try {
+            while ($response = array_shift($responses)) {
+                try {
+                    unset($response);
+                    $this->fail(TransportExceptionInterface::class.' expected');
+                } catch (TransportExceptionInterface $e) {
+                }
+            }
+
+            $duration = microtime(true) - $start;
+
+            $this->assertLessThan(1.0, $duration);
+        } finally {
+            $p1->stop();
+            $p2->stop();
+        }
+    }
+
     public function testDestruct()
     {
         $client = $this->getHttpClient(__FUNCTION__);