diff --git a/src/tomli/_parser.py b/src/tomli/_parser.py
index 11ef4533..3038891a 100644
--- a/src/tomli/_parser.py
+++ b/src/tomli/_parser.py
@@ -580,6 +580,8 @@ def parse_basic_str_escape(
             pos += 1
         pos = skip_chars(src, pos, TOML_WS_AND_NEWLINE)
         return pos, ""
+    if escape_id == "\\x":
+        return parse_hex_char(src, pos, 2)
     if escape_id == "\\u":
         return parse_hex_char(src, pos, 4)
     if escape_id == "\\U":
diff --git a/tests/data/valid/multiline-basic-str/replacements.json b/tests/data/valid/multiline-basic-str/replacements.json
index 0afb39d9..699f5562 100644
--- a/tests/data/valid/multiline-basic-str/replacements.json
+++ b/tests/data/valid/multiline-basic-str/replacements.json
@@ -1,2 +1,6 @@
-{"escape":
-  {"type":"string","value":"\u001B"}}
+{
+  "escape": {"type":"string","value":"\u001B"},
+  "tab": {"type":"string","value":"\t"},
+  "upper-j": {"type":"string","value":"J"},
+  "upper-j-2": {"type":"string","value":"J"}
+}
diff --git a/tests/data/valid/multiline-basic-str/replacements.toml b/tests/data/valid/multiline-basic-str/replacements.toml
index 10d95090..fa5647e5 100644
--- a/tests/data/valid/multiline-basic-str/replacements.toml
+++ b/tests/data/valid/multiline-basic-str/replacements.toml
@@ -1 +1,4 @@
-escape = "\e"
\ No newline at end of file
+escape = "\e"
+tab = "\x09"
+upper-j = "\x4a"
+upper-j-2 = "\x4A"
diff --git a/tests/test_data.py b/tests/test_data.py
index 490ba51b..f268ce9f 100644
--- a/tests/test_data.py
+++ b/tests/test_data.py
@@ -46,11 +46,9 @@ def test_valid(self):
                 # compatible with yet.
                 if valid.stem in {
                     "no-seconds",
-                    "hex-escape",
                     "common-34",
                     "common-31",
                     "common-29",
-                    "common-12",
                 }:
                     with self.assertRaises(tomllib.TOMLDecodeError):
                         tomllib.loads(toml_str)