diff --git a/core/src/main/java/org/testcontainers/containers/wait/strategy/LogMessageWaitStrategy.java b/core/src/main/java/org/testcontainers/containers/wait/strategy/LogMessageWaitStrategy.java
index 7a095d888f2..80616805f13 100644
--- a/core/src/main/java/org/testcontainers/containers/wait/strategy/LogMessageWaitStrategy.java
+++ b/core/src/main/java/org/testcontainers/containers/wait/strategy/LogMessageWaitStrategy.java
@@ -2,12 +2,19 @@
 
 import com.github.dockerjava.api.command.LogContainerCmd;
 import lombok.SneakyThrows;
+import org.awaitility.Awaitility;
+import org.awaitility.core.TerminalFailureException;
 import org.testcontainers.containers.ContainerLaunchException;
 import org.testcontainers.containers.output.FrameConsumerResultCallback;
 import org.testcontainers.containers.output.OutputFrame;
 import org.testcontainers.containers.output.WaitingConsumer;
 
 import java.io.IOException;
+import java.time.Duration;
+import java.util.concurrent.Callable;
+import java.util.concurrent.CancellationException;
+import java.util.concurrent.ExecutionException;
+import java.util.concurrent.Future;
 import java.util.concurrent.TimeUnit;
 import java.util.concurrent.TimeoutException;
 import java.util.function.Predicate;
@@ -19,7 +26,7 @@ public class LogMessageWaitStrategy extends AbstractWaitStrategy {
     private int times = 1;
 
     @Override
-    @SneakyThrows(IOException.class)
+    @SneakyThrows({ IOException.class, InterruptedException.class })
     protected void waitUntilReady() {
         WaitingConsumer waitingConsumer = new WaitingConsumer();
 
@@ -41,9 +48,43 @@ protected void waitUntilReady() {
                 // (?s) enables line terminator matching (equivalent to Pattern.DOTALL)
                 return outputFrame.getUtf8String().matches("(?s)" + regEx);
             };
-            try {
+
+            // Run the log wait in the background, so that this thread can abort as soon as the
+            // container exits, instead of waiting for the whole startup timeout.
+            final Future<Boolean> logWaitFuture = EXECUTOR.submit(() -> {
                 waitingConsumer.waitUntil(waitPredicate, startupTimeout.getSeconds(), TimeUnit.SECONDS, times);
-            } catch (TimeoutException e) {
+                return true;
+            });
+
+            final Callable<Boolean> logWaitComplete = logWaitFuture::isDone;
+            try {
+                Awaitility
+                    .await()
+                    .pollInSameThread()
+                    .pollInterval(Duration.ofMillis(100))
+                    .pollDelay(Duration.ZERO)
+                    .failFast("container is no longer running", () -> !waitStrategyTarget.isRunning())
+                    .forever()
+                    .until(logWaitComplete);
+            } catch (TerminalFailureException e) {
+                // The container exited while we were still waiting. Give the log wait a brief grace
+                // period to match any output that was buffered right before the container exited,
+                // before failing fast.
+                try {
+                    logWaitFuture.get(1, TimeUnit.SECONDS);
+                    return;
+                } catch (TimeoutException | ExecutionException | CancellationException graceException) {
+                    throw new IllegalStateException(
+                        "Container stopped before the expected log output matching '" + regEx + "' was produced"
+                    );
+                } finally {
+                    logWaitFuture.cancel(true);
+                }
+            }
+
+            try {
+                logWaitFuture.get(0, TimeUnit.SECONDS);
+            } catch (ExecutionException | TimeoutException | CancellationException e) {
                 throw new ContainerLaunchException("Timed out waiting for log output matching '" + regEx + "'");
             }
         }
diff --git a/core/src/test/java/org/testcontainers/containers/wait/strategy/LogMessageWaitStrategyTest.java b/core/src/test/java/org/testcontainers/containers/wait/strategy/LogMessageWaitStrategyTest.java
new file mode 100644
index 00000000000..ac352a744bb
--- /dev/null
+++ b/core/src/test/java/org/testcontainers/containers/wait/strategy/LogMessageWaitStrategyTest.java
@@ -0,0 +1,58 @@
+package org.testcontainers.containers.wait.strategy;
+
+import org.junit.jupiter.api.Test;
+import org.testcontainers.containers.ContainerLaunchException;
+import org.testcontainers.containers.GenericContainer;
+
+import java.time.Duration;
+import java.time.Instant;
+
+import static org.assertj.core.api.Assertions.assertThat;
+import static org.assertj.core.api.Assertions.catchThrowable;
+
+class LogMessageWaitStrategyTest {
+
+    @Test
+    void shouldFailFastWhenContainerExitsBeforeExpectedLogOutput() {
+        GenericContainer<?> container = new GenericContainer<>("alpine:3.20")
+            .withCommand("sh", "-c", "echo started; sleep 2; exit 1")
+            .waitingFor(Wait.forLogMessage(".*never.*", 1).withStartupTimeout(Duration.ofSeconds(60)));
+
+        Instant start = Instant.now();
+        Throwable thrown = catchThrowable(container::start);
+        Duration elapsed = Duration.between(start, Instant.now());
+
+        assertThat(thrown)
+            .as("Container launch fails when the container exits before producing the expected log output")
+            .isInstanceOf(ContainerLaunchException.class)
+            .hasRootCauseMessage("Container stopped before the expected log output matching '.*never.*' was produced");
+        assertThat(elapsed)
+            .as("Fails fast instead of waiting for the whole startup timeout")
+            .isLessThan(Duration.ofSeconds(20));
+    }
+
+    @Test
+    void shouldStillTimeOutWhenContainerKeepsRunningWithoutExpectedLogOutput() {
+        GenericContainer<?> container = new GenericContainer<>("alpine:3.20")
+            .withCommand("sh", "-c", "sleep 30")
+            .waitingFor(Wait.forLogMessage(".*never.*", 1).withStartupTimeout(Duration.ofSeconds(3)));
+
+        Throwable thrown = catchThrowable(container::start);
+
+        assertThat(thrown)
+            .as("Timeout semantics for a still running container are unchanged")
+            .isInstanceOf(ContainerLaunchException.class)
+            .hasRootCauseMessage("Timed out waiting for log output matching '.*never.*'");
+    }
+
+    @Test
+    void shouldSucceedWhenExpectedLogOutputAppearsWhileContainerIsRunning() {
+        GenericContainer<?> container = new GenericContainer<>("alpine:3.20")
+            .withCommand("sh", "-c", "echo ready; sleep 5")
+            .waitingFor(Wait.forLogMessage(".*ready.*", 1).withStartupTimeout(Duration.ofSeconds(30)));
+
+        container.start();
+
+        assertThat(container.isRunning()).isTrue();
+    }
+}