diff --git a/docs/mkdocs/docs/api/basic_json/merge_patch.md b/docs/mkdocs/docs/api/basic_json/merge_patch.md
index 1718c9227..712244022 100644
--- a/docs/mkdocs/docs/api/basic_json/merge_patch.md
+++ b/docs/mkdocs/docs/api/basic_json/merge_patch.md
@@ -37,6 +37,22 @@ Thereby, `Target` is the current object; that is, the patch is applied to the cu
 
 Linear in the lengths of `apply_patch`.
 
+## Notes
+
+!!! danger "Undefined behavior"
+
+    `merge_patch()` reads `apply_patch` while it modifies `#!cpp *this`. `apply_patch` must not be `#!cpp *this`
+    itself and must not refer to a value contained in `#!cpp *this` (for example, a subobject returned by
+    `#!cpp (*this)[key]`). Calling `merge_patch()` with such an argument reads the argument after it has been
+    invalidated by the modification, which is undefined behavior. If the patch may alias `#!cpp *this`, pass a copy
+    instead:
+
+    ```cpp
+    j.merge_patch(json(j));  // instead of j.merge_patch(j)
+    ```
+
+    See [GitHub issue #5641](https://github.com/nlohmann/json/issues/5641) for more information.
+
 ## Examples
 
 ??? example
@@ -61,3 +77,5 @@ Linear in the lengths of `apply_patch`.
 ## Version history
 
 - Added in version 3.0.0.
+- Documented that `apply_patch` must not be `#!cpp *this` or refer to a value contained in `#!cpp *this`, in version
+  3.13.0.
diff --git a/docs/mkdocs/docs/api/basic_json/update.md b/docs/mkdocs/docs/api/basic_json/update.md
index b34140dbc..56d8aa1e4 100644
--- a/docs/mkdocs/docs/api/basic_json/update.md
+++ b/docs/mkdocs/docs/api/basic_json/update.md
@@ -59,6 +59,22 @@ Basic guarantee: if an exception is thrown during the operation, the JSON value
 1. O(N*log(size() + N)), where N is the number of elements to insert.
 2. O(N*log(size() + N)), where N is the number of elements to insert.
 
+## Notes
+
+!!! danger "Undefined behavior"
+
+    Both overloads read the argument while they modify `#!cpp *this`. The argument `j` (or, for overload (2), the
+    range `[first, last)`) must not be `#!cpp *this` itself and must not refer to a value contained in
+    `#!cpp *this` (for example, a subobject returned by `#!cpp (*this)[key]`). Calling `update()` with such an
+    argument reads the argument after it has been invalidated by the modification, which is undefined behavior. If
+    the argument may alias `#!cpp *this`, pass a copy instead:
+
+    ```cpp
+    j.update(json(j["defaults"]));  // instead of j.update(j["defaults"])
+    ```
+
+    See [GitHub issue #5641](https://github.com/nlohmann/json/issues/5641) for more information.
+
 ## Examples
 
 ??? example
@@ -155,3 +171,5 @@ Basic guarantee: if an exception is thrown during the operation, the JSON value
 
 - Added in version 3.0.0.
 - Added `merge_objects` parameter in 3.10.5.
+- Documented that the argument must not be `#!cpp *this` or refer to a value contained in `#!cpp *this`, in version
+  3.13.0.