diff --git a/_pytest/debugging.py b/_pytest/debugging.py
index d7dca7809..e458406b5 100644
--- a/_pytest/debugging.py
+++ b/_pytest/debugging.py
@@ -95,13 +95,17 @@ def _enter_pdb(node, excinfo, rep):
 
 
 def _postmortem_traceback(excinfo):
-    # A doctest.UnexpectedException is not useful for post_mortem.
-    # Use the underlying exception instead:
-    from doctest import UnexpectedException
-    if isinstance(excinfo.value, UnexpectedException):
-        return excinfo.value.exc_info[2]
-    else:
-        return excinfo._excinfo[2]
+    try:
+        from doctest import UnexpectedException
+        if isinstance(excinfo.value, UnexpectedException):
+            # A doctest.UnexpectedException is not useful for post_mortem.
+            # Use the underlying exception instead:
+            return excinfo.value.exc_info[2]
+    except ImportError:
+        # If we fail to import, continue quietly (if we ran out of file descriptors, for example: #1810)
+        pass
+
+    return excinfo._excinfo[2]
 
 
 def _find_last_non_hidden_frame(stack):
diff --git a/changelog/1810.bugfix b/changelog/1810.bugfix
new file mode 100644
index 000000000..6e9389671
--- /dev/null
+++ b/changelog/1810.bugfix
@@ -0,0 +1 @@
+If we fail to import doctest.UnexpectedException during postmortem, fail quietly and continue.
\ No newline at end of file