diff --git a/testcontainers/src/core/client.rs b/testcontainers/src/core/client.rs
index 6878b5b6..92d36c26 100644
--- a/testcontainers/src/core/client.rs
+++ b/testcontainers/src/core/client.rs
@@ -127,6 +127,11 @@ impl Client {
             .into_stderr()
     }
 
+    pub(crate) fn both_std_logs(&self, id: &str, follow: bool) -> RawLogStream {
+        self.logs_stream(id, Some(LogSource::BothStd), follow)
+            .into_both_std()
+    }
+
     pub(crate) fn logs(&self, id: &str, follow: bool) -> LogStream {
         self.logs_stream(id, None, follow)
     }
@@ -266,8 +271,12 @@ impl Client {
     ) -> LogStream {
         let options = LogsOptions {
             follow,
-            stdout: source_filter.map(LogSource::is_stdout).unwrap_or(true),
-            stderr: source_filter.map(LogSource::is_stderr).unwrap_or(true),
+            stdout: source_filter
+                .map(LogSource::includes_stdout)
+                .unwrap_or(true),
+            stderr: source_filter
+                .map(LogSource::includes_stderr)
+                .unwrap_or(true),
             tail: "all".to_owned(),
             ..Default::default()
         };
diff --git a/testcontainers/src/core/logs.rs b/testcontainers/src/core/logs.rs
index 8eb85bcc..29d481a8 100644
--- a/testcontainers/src/core/logs.rs
+++ b/testcontainers/src/core/logs.rs
@@ -29,15 +29,16 @@ pub enum WaitLogError {
 pub enum LogSource {
     StdOut,
     StdErr,
+    BothStd,
 }
 
 impl LogSource {
-    pub(super) fn is_stdout(self) -> bool {
-        matches!(self, Self::StdOut)
+    pub(super) fn includes_stdout(self) -> bool {
+        matches!(self, Self::StdOut | Self::BothStd)
     }
 
-    pub(super) fn is_stderr(self) -> bool {
-        matches!(self, Self::StdErr)
+    pub(super) fn includes_stderr(self) -> bool {
+        matches!(self, Self::StdErr | Self::BothStd)
     }
 }
 
diff --git a/testcontainers/src/core/logs/stream.rs b/testcontainers/src/core/logs/stream.rs
index 4299ca67..3343ed55 100644
--- a/testcontainers/src/core/logs/stream.rs
+++ b/testcontainers/src/core/logs/stream.rs
@@ -6,7 +6,7 @@ use std::{
 };
 
 use bytes::Bytes;
-use futures::{stream::BoxStream, Stream, StreamExt};
+use futures::{stream::BoxStream, Stream, StreamExt, TryStreamExt};
 use tokio_stream::wrappers::UnboundedReceiverStream;
 
 use crate::core::logs::LogFrame;
@@ -51,6 +51,16 @@ impl LogStream {
             .boxed()
     }
 
+    /// Log stream with messages from bith stdout and stderr.
+    pub(crate) fn into_both_std(self) -> RawLogStream {
+        self.inner
+            .map_ok(|frame| match frame {
+                LogFrame::StdErr(bytes) => bytes,
+                LogFrame::StdOut(bytes) => bytes,
+            })
+            .boxed()
+    }
+
     /// Splits the log stream into two streams, one for stdout and one for stderr.
     pub(crate) async fn split(self) -> (RawLogStream, RawLogStream) {
         let (stdout_tx, stdout_rx) = tokio::sync::mpsc::unbounded_channel();
diff --git a/testcontainers/src/core/wait/log_strategy.rs b/testcontainers/src/core/wait/log_strategy.rs
index 6347bdbf..259811c7 100644
--- a/testcontainers/src/core/wait/log_strategy.rs
+++ b/testcontainers/src/core/wait/log_strategy.rs
@@ -30,6 +30,13 @@ impl LogWaitStrategy {
         Self::new(LogSource::StdErr, message)
     }
 
+    /// Create a new [`LogWaitStrategy`] that waits for the given message to appear in either
+    /// standard output logs or standard error logs.
+    /// Shortcut for `LogWaitStrategy::new(LogSource::BothStd, message)`.
+    pub fn stdout_or_stderr(message: impl AsRef<[u8]>) -> Self {
+        Self::new(LogSource::BothStd, message)
+    }
+
     /// Create a new `LogWaitStrategy` with the given log source and message.
     /// The message is expected to appear in the logs exactly once by default.
     pub fn new(source: LogSource, message: impl AsRef<[u8]>) -> Self {
@@ -56,6 +63,7 @@ impl WaitStrategy for LogWaitStrategy {
         let log_stream = match self.source {
             LogSource::StdOut => client.stdout_logs(container.id(), true),
             LogSource::StdErr => client.stderr_logs(container.id(), true),
+            LogSource::BothStd => client.both_std_logs(container.id(), true),
         };
 
         WaitingStreamWrapper::new(log_stream)
diff --git a/testcontainers/src/core/wait/mod.rs b/testcontainers/src/core/wait/mod.rs
index d6752a47..3f506170 100644
--- a/testcontainers/src/core/wait/mod.rs
+++ b/testcontainers/src/core/wait/mod.rs
@@ -57,6 +57,11 @@ impl WaitFor {
         Self::log(LogWaitStrategy::new(LogSource::StdErr, message))
     }
 
+    /// Wait for the message to appear on either container's stdout or stderr.
+    pub fn message_on_either_std(message: impl AsRef<[u8]>) -> WaitFor {
+        Self::log(LogWaitStrategy::new(LogSource::BothStd, message))
+    }
+
     /// Wait for the message to appear on the container's stdout.
     pub fn log(log_strategy: LogWaitStrategy) -> WaitFor {
         WaitFor::Log(log_strategy)