diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 2aac2596c18cb..b4289973a26cd 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -296,6 +296,7 @@ I/O
 - :meth:`to_csv` did not support zip compression for binary file object not having a filename (:issue: `35058`)
 - :meth:`to_csv` and :meth:`read_csv` did not honor `compression` and `encoding` for path-like objects that are internally converted to file-like objects (:issue:`35677`, :issue:`26124`, and :issue:`32392`)
 - :meth:`to_picke` and :meth:`read_pickle` did not support compression for file-objects (:issue:`26237`, :issue:`29054`, and :issue:`29570`)
+- Bug in :meth:`read_excel` with `engine="odf"` caused ``UnboundLocalError`` in some cases where cells had nested child nodes (:issue:`36122`, and :issue:`35802`)
 
 Plotting
 ^^^^^^^^
diff --git a/pandas/io/excel/_odfreader.py b/pandas/io/excel/_odfreader.py
index 02575ab878f6e..09a4bfb9accc3 100644
--- a/pandas/io/excel/_odfreader.py
+++ b/pandas/io/excel/_odfreader.py
@@ -197,22 +197,24 @@ def _get_cell_string_value(self, cell) -> str:
         Find and decode OpenDocument text:s tags that represent
         a run length encoded sequence of space characters.
         """
-        from odf.element import Element, Text
+        from odf.element import Element
         from odf.namespaces import TEXTNS
-        from odf.text import P, S
+        from odf.text import S
 
-        text_p = P().qname
         text_s = S().qname
 
-        p = cell.childNodes[0]
-
         value = []
-        if p.qname == text_p:
-            for k, fragment in enumerate(p.childNodes):
-                if isinstance(fragment, Text):
-                    value.append(fragment.data)
-                elif isinstance(fragment, Element):
-                    if fragment.qname == text_s:
-                        spaces = int(fragment.attributes.get((TEXTNS, "c"), 1))
+
+        for fragment in cell.childNodes:
+            if isinstance(fragment, Element):
+                if fragment.qname == text_s:
+                    spaces = int(fragment.attributes.get((TEXTNS, "c"), 1))
                     value.append(" " * spaces)
+                else:
+                    # recursive impl needed in case of nested fragments
+                    # with multiple spaces
+                    # https://github.com/pandas-dev/pandas/pull/36175#discussion_r484639704
+                    value.append(self._get_cell_string_value(fragment))
+            else:
+                value.append(str(fragment))
         return "".join(value)
diff --git a/pandas/tests/io/data/excel/gh-35802.ods b/pandas/tests/io/data/excel/gh-35802.ods
new file mode 100755
index 0000000000000..f3ad061f1d995
Binary files /dev/null and b/pandas/tests/io/data/excel/gh-35802.ods differ
diff --git a/pandas/tests/io/data/excel/gh-36122.ods b/pandas/tests/io/data/excel/gh-36122.ods
new file mode 100755
index 0000000000000..3dfdaf976da45
Binary files /dev/null and b/pandas/tests/io/data/excel/gh-36122.ods differ
diff --git a/pandas/tests/io/excel/test_readers.py b/pandas/tests/io/excel/test_readers.py
index 431a50477fccc..33467be42dfd9 100644
--- a/pandas/tests/io/excel/test_readers.py
+++ b/pandas/tests/io/excel/test_readers.py
@@ -499,6 +499,23 @@ def test_reader_spaces(self, read_ext):
         )
         tm.assert_frame_equal(actual, expected)
 
+    # gh-36122, gh-35802
+    @pytest.mark.parametrize(
+        "basename,expected",
+        [
+            ("gh-35802", DataFrame({"COLUMN": ["Test (1)"]})),
+            ("gh-36122", DataFrame(columns=["got 2nd sa"])),
+        ],
+    )
+    def test_read_excel_ods_nested_xml(self, read_ext, basename, expected):
+        # see gh-35802
+        engine = pd.read_excel.keywords["engine"]
+        if engine != "odf":
+            pytest.skip(f"Skipped for engine: {engine}")
+
+        actual = pd.read_excel(basename + read_ext)
+        tm.assert_frame_equal(actual, expected)
+
     def test_reading_all_sheets(self, read_ext):
         # Test reading all sheet names by setting sheet_name to None,
         # Ensure a dict is returned.