diff --git a/omegaconf/dictconfig.py b/omegaconf/dictconfig.py
index 8e25ce9c2..10a3b7f34 100644
--- a/omegaconf/dictconfig.py
+++ b/omegaconf/dictconfig.py
@@ -594,6 +594,8 @@ def __eq__(self, other: Any) -> bool:
             return DictConfig._dict_conf_eq(self, other)
         if isinstance(other, DictConfig):
             return DictConfig._dict_conf_eq(self, other)
+        if self._is_missing():
+            return _is_missing_literal(other)
         return NotImplemented
 
     def __ne__(self, other: Any) -> bool:
diff --git a/omegaconf/listconfig.py b/omegaconf/listconfig.py
index bb2c8a886..08a7d4e38 100644
--- a/omegaconf/listconfig.py
+++ b/omegaconf/listconfig.py
@@ -16,6 +16,7 @@
 
 from ._utils import (
     ValueKind,
+    _is_missing_literal,
     _is_none,
     _is_optional,
     format_and_raise,
@@ -481,6 +482,8 @@ def __eq__(self, other: Any) -> bool:
             return ListConfig._list_eq(self, other)
         if other is None or isinstance(other, ListConfig):
             return ListConfig._list_eq(self, other)
+        if self._is_missing():
+            return _is_missing_literal(other)
         return NotImplemented
 
     def __ne__(self, other: Any) -> bool:
diff --git a/tests/test_config_eq.py b/tests/test_config_eq.py
index 003506be6..dae24de0b 100644
--- a/tests/test_config_eq.py
+++ b/tests/test_config_eq.py
@@ -99,6 +99,20 @@ def eq(a: Any, b: Any) -> None:
     eq(c2, i2)
 
 
+@mark.parametrize(
+    "cfg,other",
+    [
+        param(DictConfig("???"), "???", id="missing_dictconfig"),
+        param(ListConfig("???"), "???", id="missing_listconfig"),
+    ],
+)
+def test_missing_container_string_eq(cfg: Any, other: Any) -> None:
+    assert cfg == other
+    assert other == cfg
+    assert not (cfg != other)
+    assert not (other != cfg)
+
+
 @mark.parametrize(
     "input1, input2",
     [