diff --git a/CHANGELOG.md b/CHANGELOG.md
index 536f2c4..ffb11bc 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -22,6 +22,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 - `ProcessJobExecutor`
 	- subprocess errors include exit code
 	- logs unexpected stdout instead of triggering E_USER_NOTICE (via optional logger)
+	- logs unexpected stderr instead of throwing an exception (via optional logger)
 
 ### Fixed
 
diff --git a/docs/README.md b/docs/README.md
index 3d2be68..36002f6 100644
--- a/docs/README.md
+++ b/docs/README.md
@@ -376,7 +376,9 @@ $scheduler = new SimpleScheduler(null, null, null, null, $logger);
 
 If you use [process job executor](#parallelization-and-process-isolation), then also these situations are logged:
 
-- Subprocess running the job produced unexpected stdout output. Job should never echo or write directly to stdout.
+- Subprocess running the job produced unexpected *stdout* output. Job should never echo or write directly to stdout.
+- Subprocess running the job produced unexpected *stderr* output. This may happen just due to deprecation notices but may
+  also be caused by more serious problem occurring in CLI.
 
 ```php
 use Orisai\Scheduler\SimpleScheduler;
diff --git a/src/Executor/ProcessJobExecutor.php b/src/Executor/ProcessJobExecutor.php
index 3ddc2fc..8026a83 100644
--- a/src/Executor/ProcessJobExecutor.php
+++ b/src/Executor/ProcessJobExecutor.php
@@ -101,17 +101,17 @@ public function runJobs(
 
 				unset($jobExecutions[$i]);
 
-				$output = trim($execution->getOutput());
-				$errorOutput = trim($execution->getErrorOutput());
+				$stdout = trim($execution->getOutput());
+				$stderr = trim($execution->getErrorOutput());
 
 				try {
-					$decoded = json_decode($output, true, 512, JSON_THROW_ON_ERROR);
+					$decoded = json_decode($stdout, true, 512, JSON_THROW_ON_ERROR);
 					assert(is_array($decoded));
 				} catch (JsonException $e) {
 					$suppressedExceptions[] = $this->createSubprocessFail(
 						$execution,
-						$output,
-						$errorOutput,
+						$stdout,
+						$stderr,
 					);
 
 					continue;
@@ -122,11 +122,8 @@ public function runJobs(
 					$this->logUnexpectedStdout($execution, $jobId, $unexpectedStdout);
 				}
 
-				if ($errorOutput !== '') {
-					$suppressedExceptions[] = $this->createStderrFail(
-						$execution,
-						$errorOutput,
-					);
+				if ($stderr !== '') {
+					$this->logUnexpectedStderr($execution, $jobId, $stderr);
 				}
 
 				yield $jobSummaries[] = $this->createSummary($decoded, $jobSchedule->getExpression());
@@ -208,16 +205,17 @@ private function createSubprocessFail(Process $execution, string $output, string
 			->withMessage($message);
 	}
 
-	private function createStderrFail(Process $execution, string $errorOutput): JobProcessFailure
+	/**
+	 * @param int|string $jobId
+	 */
+	private function logUnexpectedStderr(Process $execution, $jobId, string $stderr): void
 	{
-		$message = Message::create()
-			->withContext("Running job via command {$execution->getCommandLine()}")
-			->withProblem('Job subprocess produced stderr output.')
-			->with('Exit code', (string) $execution->getExitCode())
-			->with('stderr', $errorOutput);
-
-		return JobProcessFailure::create()
-			->withMessage($message);
+		$this->logger->warning("Subprocess running job '$jobId' produced unexpected stderr output.", [
+			'id' => $jobId,
+			'command' => $execution->getCommandLine(),
+			'exitCode' => $execution->getExitCode(),
+			'stderr' => $stderr,
+		]);
 	}
 
 	/**
diff --git a/tests/Unit/SchedulerProcessSetup.php b/tests/Unit/SchedulerProcessSetup.php
index e2d48a9..c134f6f 100644
--- a/tests/Unit/SchedulerProcessSetup.php
+++ b/tests/Unit/SchedulerProcessSetup.php
@@ -84,11 +84,15 @@ public static function createWithStderr(): ManagedScheduler
 		return new ManagedScheduler($jobManager, null, null, $executor, $clock);
 	}
 
-	public static function createWithStderrJob(): ManagedScheduler
+	/**
+	 * @return array{ManagedScheduler, TestLogger}
+	 */
+	public static function createWithStderrJob(): array
 	{
 		$jobManager = new SimpleJobManager();
 		$clock = new FrozenClock(1);
-		$executor = new ProcessJobExecutor($clock);
+		$logger = new TestLogger();
+		$executor = new ProcessJobExecutor($clock, $logger);
 		$executor->setExecutable(__DIR__ . '/scheduler-process-binary-with-stderr-job.php');
 
 		$jobManager->addJob(
@@ -98,7 +102,9 @@ public static function createWithStderrJob(): ManagedScheduler
 			new CronExpression('* * * * *'),
 		);
 
-		return new ManagedScheduler($jobManager, null, null, $executor, $clock);
+		$scheduler = new ManagedScheduler($jobManager, null, null, $executor, $clock, $logger);
+
+		return [$scheduler, $logger];
 	}
 
 	/**
diff --git a/tests/Unit/SimpleSchedulerTest.php b/tests/Unit/SimpleSchedulerTest.php
index 3ea95f1..d7f7f72 100644
--- a/tests/Unit/SimpleSchedulerTest.php
+++ b/tests/Unit/SimpleSchedulerTest.php
@@ -1174,37 +1174,30 @@ public function testProcessStderr(): void
 
 	public function testProcessJobStderr(): void
 	{
-		$scheduler = SchedulerProcessSetup::createWithStderrJob();
+		[$scheduler, $logger] = SchedulerProcessSetup::createWithStderrJob();
+		$summary = $scheduler->run();
 
-		$e = null;
-		try {
-			$scheduler->run();
-		} catch (RunFailure $e) {
-			// Handled bellow
+		foreach ($logger->logs as &$log) {
+			self::assertIsString($log[2]['command']);
+			// Can't easily assert
+			unset($log[2]['command']);
 		}
 
-		self::assertNotNull($e);
-		self::assertStringStartsWith(
-			<<<'MSG'
-Run failed
-Suppressed errors:
-MSG,
-			$e->getMessage(),
+		self::assertCount(1, $summary->getJobSummaries());
+		self::assertSame(
+			[
+				[
+					'warning',
+					"Subprocess running job '0' produced unexpected stderr output.",
+					[
+						'id' => 0,
+						'exitCode' => 0,
+						'stderr' => 'job error',
+					],
+				],
+			],
+			$logger->logs,
 		);
-
-		self::assertNotSame([], $e->getSuppressed());
-		foreach ($e->getSuppressed() as $suppressed) {
-			self::assertInstanceOf(JobProcessFailure::class, $suppressed);
-			self::assertStringMatchesFormat(
-				<<<'MSG'
-Context: Running job via command %a
-Problem: Job subprocess produced stderr output.
-Exit code: 0
-stderr: job error
-MSG,
-				rtrim($suppressed->getMessage()),
-			);
-		}
 	}
 
 	/**
diff --git a/tests/Unit/scheduler-process-binary-with-stderr-job.php b/tests/Unit/scheduler-process-binary-with-stderr-job.php
index b61486c..5d17303 100644
--- a/tests/Unit/scheduler-process-binary-with-stderr-job.php
+++ b/tests/Unit/scheduler-process-binary-with-stderr-job.php
@@ -7,7 +7,7 @@
 require_once __DIR__ . '/../../vendor/autoload.php';
 
 $application = new Application();
-$scheduler = SchedulerProcessSetup::createWithStderrJob();
+[$scheduler] = SchedulerProcessSetup::createWithStderrJob();
 
 $command = new RunJobCommand($scheduler);