diff --git a/src/docformatter/format.py b/src/docformatter/format.py
index 584ff6a..21d8e62 100644
--- a/src/docformatter/format.py
+++ b/src/docformatter/format.py
@@ -196,8 +196,14 @@ def _do_update_token_indices(
         is_multiline = _is_multiline_parameter(tokens, i - 1)
         is_same_line = tokens[i].line == tokens[i - 1].line
         is_same_position = tokens[i].start[0] == tokens[i - 1].end[0]
-
-        if (
+        # A backslash continuation joins two physical lines without an NL
+        # token between them, so the current token always starts on the row
+        # after the previous one, even though the rows may look the same once
+        # the previous token has been shifted.
+        prev_line = tokens[i - 1].line.rstrip("\r\n")
+        is_backslash_continuation = not is_same_line and prev_line.endswith("\\")
+
+        if not is_backslash_continuation and (
             is_multiline
             or (is_same_line or is_same_position)
             and tokens[i - 1].type
diff --git a/tests/_data/string_files/do_format_code.toml b/tests/_data/string_files/do_format_code.toml
index d652a15..6928cfe 100644
--- a/tests/_data/string_files/do_format_code.toml
+++ b/tests/_data/string_files/do_format_code.toml
@@ -1260,3 +1260,14 @@ expected="def foo():\n    \"\"\"Summary.\"\"\"\n    x = 1\n    # next line has 4
 [issue_360_no_trailing_newline]
 source="def foo():\n    \"\"\"\n    Hello foo.\n    \"\"\"\n    x = 1"
 expected="def foo():\n    \"\"\"Hello foo.\"\"\"\n    x = 1"
+
+# A backslash continuation after a docstring that gets a blank line inserted
+# must not crash the tokenizer round-trip: the continuation line has no NL
+# token in front of it, so its row must be derived from the previous token.
+[issue_377_backslash_continuation]
+source="class A:\n    \"\"\"Doc.\"\"\"\n    x = 1 \\\n        + 2\n"
+expected="class A:\n    \"\"\"Doc.\"\"\"\n\n    x = 1 \\\n        + 2\n"
+
+[issue_377_module_docstring]
+source="\"\"\"Doc.\"\"\"\nx = 1 \\\n    + 2\n"
+expected="\"\"\"Doc.\"\"\"\n\nx = 1 \\\n    + 2\n"
diff --git a/tests/formatter/test_do_format_code.py b/tests/formatter/test_do_format_code.py
index 037ace1..b506e52 100644
--- a/tests/formatter/test_do_format_code.py
+++ b/tests/formatter/test_do_format_code.py
@@ -143,6 +143,8 @@
         ("issue_331_black_module_docstring", ["--black", ""]),
         ("issue_355", NO_ARGS),
         ("issue_360_no_trailing_newline", NO_ARGS),
+        ("issue_377_backslash_continuation", NO_ARGS),
+        ("issue_377_module_docstring", NO_ARGS),
     ],
 )
 def test_do_format_code(test_key, test_args, args):