diff --git a/Lib/lib2to3/Grammar.txt b/Lib/lib2to3/Grammar.txt
index e007dc188af..fa7b15061d9 100644
--- a/Lib/lib2to3/Grammar.txt
+++ b/Lib/lib2to3/Grammar.txt
@@ -18,15 +18,55 @@ decorated: decorators (classdef | funcdef | async_funcdef)
 async_funcdef: ASYNC funcdef
 funcdef: 'def' NAME parameters ['->' test] ':' suite
 parameters: '(' [typedargslist] ')'
-typedargslist: ((tfpdef ['=' test] ',')*
-                ('*' [tname] (',' tname ['=' test])* [',' ['**' tname [',']]] | '**' tname [','])
-                | tfpdef ['=' test] (',' tfpdef ['=' test])* [','])
+
+# The following definition for typedarglist is equivalent to this set of rules:
+#
+#     arguments = argument (',' argument)*
+#     argument = tfpdef ['=' test]
+#     kwargs = '**' tname [',']
+#     args = '*' [tname]
+#     kwonly_kwargs = (',' argument)* [',' [kwargs]]
+#     args_kwonly_kwargs = args kwonly_kwargs | kwargs
+#     poskeyword_args_kwonly_kwargs = arguments [',' [args_kwonly_kwargs]]
+#     typedargslist_no_posonly  = poskeyword_args_kwonly_kwargs | args_kwonly_kwargs
+#     typedarglist = arguments ',' '/' [',' [typedargslist_no_posonly]])|(typedargslist_no_posonly)"
+#
+# It needs to be fully expanded to allow our LL(1) parser to work on it.
+
+typedargslist: tfpdef ['=' test] (',' tfpdef ['=' test])* ',' '/' [
+                     ',' [((tfpdef ['=' test] ',')* ('*' [tname] (',' tname ['=' test])*
+                            [',' ['**' tname [',']]] | '**' tname [','])
+                     | tfpdef ['=' test] (',' tfpdef ['=' test])* [','])]
+                ] | ((tfpdef ['=' test] ',')* ('*' [tname] (',' tname ['=' test])*
+                     [',' ['**' tname [',']]] | '**' tname [','])
+                     | tfpdef ['=' test] (',' tfpdef ['=' test])* [','])
+
 tname: NAME [':' test]
 tfpdef: tname | '(' tfplist ')'
 tfplist: tfpdef (',' tfpdef)* [',']
-varargslist: ((vfpdef ['=' test] ',')*
-              ('*' [vname] (',' vname ['=' test])*  [',' ['**' vname [',']]] | '**' vname [','])
-              | vfpdef ['=' test] (',' vfpdef ['=' test])* [','])
+
+# The following definition for varargslist is equivalent to this set of rules:
+#
+#     arguments = argument (',' argument )*
+#     argument = vfpdef ['=' test]
+#     kwargs = '**' vname [',']
+#     args = '*' [vname]
+#     kwonly_kwargs = (',' argument )* [',' [kwargs]]
+#     args_kwonly_kwargs = args kwonly_kwargs | kwargs
+#     poskeyword_args_kwonly_kwargs = arguments [',' [args_kwonly_kwargs]]
+#     vararglist_no_posonly = poskeyword_args_kwonly_kwargs | args_kwonly_kwargs
+#     varargslist = arguments ',' '/' [','[(vararglist_no_posonly)]] | (vararglist_no_posonly)
+#
+# It needs to be fully expanded to allow our LL(1) parser to work on it.
+
+varargslist: vfpdef ['=' test ](',' vfpdef ['=' test])* ',' '/' [',' [
+                     ((vfpdef ['=' test] ',')* ('*' [vname] (',' vname ['=' test])*
+                            [',' ['**' vname [',']]] | '**' vname [','])
+                            | vfpdef ['=' test] (',' vfpdef ['=' test])* [','])
+                     ]] | ((vfpdef ['=' test] ',')*
+                     ('*' [vname] (',' vname ['=' test])*  [',' ['**' vname [',']]]| '**' vname [','])
+                     | vfpdef ['=' test] (',' vfpdef ['=' test])* [','])
+
 vname: NAME
 vfpdef: vname | '(' vfplist ')'
 vfplist: vfpdef (',' vfpdef)* [',']
diff --git a/Lib/lib2to3/tests/test_parser.py b/Lib/lib2to3/tests/test_parser.py
index ba2bb787332..d5db66b9b1e 100644
--- a/Lib/lib2to3/tests/test_parser.py
+++ b/Lib/lib2to3/tests/test_parser.py
@@ -272,6 +272,12 @@ class TestUnpackingGeneralizations(GrammarTest):
     def test_dict_display_2(self):
         self.validate("""{**{}, 3:4, **{5:6, 7:8}}""")
 
+    def test_complex_star_expression(self):
+        self.validate("func(* [] or [1])")
+
+    def test_complex_double_star_expression(self):
+        self.validate("func(**{1: 3} if False else {x: x for x in range(3)})")
+
     def test_argument_unpacking_1(self):
         self.validate("""f(a, *b, *c, d)""")
 
@@ -630,6 +636,7 @@ class TestLiterals(GrammarTest):
 
 
 class TestNamedAssignments(GrammarTest):
+    """Also known as the walrus operator."""
 
     def test_named_assignment_if(self):
         driver.parse_string("if f := x(): pass\n")
@@ -644,6 +651,30 @@ class TestNamedAssignments(GrammarTest):
         driver.parse_string("[(lastNum := num) == 1 for num in [1, 2, 3]]\n")
 
 
+class TestPositionalOnlyArgs(GrammarTest):
+
+    def test_one_pos_only_arg(self):
+        driver.parse_string("def one_pos_only_arg(a, /): pass\n")
+
+    def test_all_markers(self):
+        driver.parse_string(
+                "def all_markers(a, b=2, /, c, d=4, *, e=5, f): pass\n")
+
+    def test_all_with_args_and_kwargs(self):
+        driver.parse_string(
+                """def all_markers_with_args_and_kwargs(
+                           aa, b, /, _cc, d, *args, e, f_f, **kwargs,
+                   ):
+                       pass\n""")
+
+    def test_lambda_soup(self):
+        driver.parse_string(
+                "lambda a, b, /, c, d, *args, e, f, **kw: kw\n")
+
+    def test_only_positional_or_keyword(self):
+        driver.parse_string("def func(a,b,/,*,g,e=3): pass\n")
+
+
 class TestPickleableException(unittest.TestCase):
     def test_ParseError(self):
         err = ParseError('msg', 2, None, (1, 'context'))
diff --git a/Misc/NEWS.d/next/Library/2020-12-14-08-23-57.bpo-36541.qdEtZv.rst b/Misc/NEWS.d/next/Library/2020-12-14-08-23-57.bpo-36541.qdEtZv.rst
new file mode 100644
index 00000000000..5678d8c595c
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-12-14-08-23-57.bpo-36541.qdEtZv.rst
@@ -0,0 +1,2 @@
+Fixed lib2to3.pgen2 to be able to parse PEP-570 positional only argument
+syntax.