diff --git a/changelogs/fragments/1158-select-fix.yml b/changelogs/fragments/1158-select-fix.yml
new file mode 100644
index 00000000..83cc14cc
--- /dev/null
+++ b/changelogs/fragments/1158-select-fix.yml
@@ -0,0 +1,3 @@
+bugfixes:
+  - "docker, nsenter connection plugins - fix handling of ``become`` plugin password prompt handling in case multiple events arrive at the same time
+     (https://github.com/ansible-collections/community.docker/pull/1158)."
diff --git a/plugins/connection/docker.py b/plugins/connection/docker.py
index 252f6451..5ff2f0b4 100644
--- a/plugins/connection/docker.py
+++ b/plugins/connection/docker.py
@@ -388,16 +388,21 @@ class Connection(ConnectionBase):
                         stdout, stderr = p.communicate()
                         raise AnsibleError('timeout waiting for privilege escalation password prompt:\n' + to_native(become_output))
 
+                    chunks = b""
                     for key, event in events:
                         if key.fileobj == p.stdout:
                             chunk = p.stdout.read()
+                            if chunk:
+                                chunks += chunk
                         elif key.fileobj == p.stderr:
                             chunk = p.stderr.read()
+                            if chunk:
+                                chunks += chunk
 
-                    if not chunk:
+                    if not chunks:
                         stdout, stderr = p.communicate()
                         raise AnsibleError('privilege output closed while waiting for password prompt:\n' + to_native(become_output))
-                    become_output += chunk
+                    become_output += chunks
             finally:
                 selector.close()
 
diff --git a/plugins/connection/nsenter.py b/plugins/connection/nsenter.py
index ccc660b9..9fc65490 100644
--- a/plugins/connection/nsenter.py
+++ b/plugins/connection/nsenter.py
@@ -170,16 +170,21 @@ class Connection(ConnectionBase):
                         stdout, stderr = p.communicate()
                         raise AnsibleError('timeout waiting for privilege escalation password prompt:\n' + to_native(become_output))
 
+                    chunks = b""
                     for key, event in events:
                         if key.fileobj == p.stdout:
                             chunk = p.stdout.read()
+                            if chunk:
+                                chunks += chunk
                         elif key.fileobj == p.stderr:
                             chunk = p.stderr.read()
+                            if chunk:
+                                chunks += chunk
 
-                    if not chunk:
+                    if not chunks:
                         stdout, stderr = p.communicate()
                         raise AnsibleError('privilege output closed while waiting for password prompt:\n' + to_native(become_output))
-                    become_output += chunk
+                    become_output += chunks
             finally:
                 selector.close()