diff --git a/prometheus_client/openmetrics/parser.py b/prometheus_client/openmetrics/parser.py
index 50fa3419..fe4d90cd 100644
--- a/prometheus_client/openmetrics/parser.py
+++ b/prometheus_client/openmetrics/parser.py
@@ -72,7 +72,7 @@ def _unescape_help(text):
 
 def _parse_value(value):
     value = ''.join(value)
-    if value != value.strip():
+    if value != value.strip() or '_' in value:
         raise ValueError("Invalid value: {0!r}".format(value))
     try:
         return int(value)
@@ -84,7 +84,7 @@ def _parse_timestamp(timestamp):
     timestamp = ''.join(timestamp)
     if not timestamp:
         return None
-    if timestamp != timestamp.strip():
+    if timestamp != timestamp.strip() or '_' in timestamp:
         raise ValueError("Invalid timestamp: {0!r}".format(timestamp))
     try:
         # Simple int.
diff --git a/tests/openmetrics/test_parser.py b/tests/openmetrics/test_parser.py
index 63dd5e42..b5585762 100644
--- a/tests/openmetrics/test_parser.py
+++ b/tests/openmetrics/test_parser.py
@@ -53,6 +53,22 @@ def test_float_gauge(self):
 """)
         self.assertEqual([GaugeMetricFamily("a", "help", value=1.2)], list(families))
 
+    def test_leading_zeros_simple_gauge(self):
+        families = text_string_to_metric_families("""# TYPE a gauge
+# HELP a help
+a 0000000000000000000000000000000000000000001
+# EOF
+""")
+        self.assertEqual([GaugeMetricFamily("a", "help", value=1)], list(families))
+
+    def test_leading_zeros_float_gauge(self):
+        families = text_string_to_metric_families("""# TYPE a gauge
+# HELP a help
+a 0000000000000000000000000000000000000000001.2e-1
+# EOF
+""")
+        self.assertEqual([GaugeMetricFamily("a", "help", value=.12)], list(families))
+
     def test_nan_gauge(self):
         families = text_string_to_metric_families("""# TYPE a gauge
 # HELP a help
@@ -610,14 +626,25 @@ def test_invalid_input(self):
             ('a  1\n# EOF\n'),
             ('a 1\t\n# EOF\n'),
             ('a 1 \n# EOF\n'),
+            ('a 1_2\n# EOF\n'),
+            ('a 0x1p-3\n# EOF\n'),
+            ('a 0x1P-3\n# EOF\n'),
+            ('a 0b1\n# EOF\n'),
+            ('a 0B1\n# EOF\n'),
+            ('a 0x1\n# EOF\n'),
+            ('a 0X1\n# EOF\n'),
+            ('a 0o1\n# EOF\n'),
+            ('a 0O1\n# EOF\n'),
             # Bad timestamp.
             ('a 1 z\n# EOF\n'),
             ('a 1 1z\n# EOF\n'),
+            ('a 1 1_2\n# EOF\n'),
             ('a 1 1.1.1\n# EOF\n'),
             ('a 1 NaN\n# EOF\n'),
             ('a 1 Inf\n# EOF\n'),
             ('a 1 +Inf\n# EOF\n'),
             ('a 1 -Inf\n# EOF\n'),
+            ('a 1 0x1p-3\n# EOF\n'),
             # Bad exemplars.
             ('# TYPE a histogram\na_bucket{le="+Inf"} 1 #\n# EOF\n'),
             ('# TYPE a histogram\na_bucket{le="+Inf"} 1# {} 1\n# EOF\n'),
@@ -627,6 +654,8 @@ def test_invalid_input(self):
             ('# TYPE a histogram\na_bucket{le="+Inf"} 1 # {} 1 1 \n# EOF\n'),
             ('# TYPE a histogram\na_bucket{le="+Inf"} 1 # '
              '{a="2345678901234567890123456789012345678901234567890123456789012345"} 1 1\n# EOF\n'),
+            ('# TYPE a histogram\na_bucket{le="+Inf"} 1 # {} 0x1p-3\n# EOF\n'),
+            ('# TYPE a histogram\na_bucket{le="+Inf"} 1 # {} 1 0x1p-3\n# EOF\n'),
             # Exemplars on unallowed samples.
             ('# TYPE a histogram\na_sum 1 # {a="b"} 0.5\n# EOF\n'),
             ('# TYPE a gaugehistogram\na_sum 1 # {a="b"} 0.5\n# EOF\n'),
@@ -695,7 +724,7 @@ def test_invalid_input(self):
             ('# TYPE a gauge\na 0\na 0 0\n# EOF\n'),
             ('# TYPE a gauge\na 0 0\na 0\n# EOF\n'),
         ]:
-            with self.assertRaises(ValueError):
+            with self.assertRaises(ValueError, msg=case):
                 list(text_string_to_metric_families(case))
 
     @unittest.skipIf(sys.version_info < (2, 7), "float repr changed from 2.6 to 2.7")