diff --git a/src/go/internal/gccgoimporter/importer_test.go b/src/go/internal/gccgoimporter/importer_test.go
index ee01883..21a3bcb 100644
--- a/src/go/internal/gccgoimporter/importer_test.go
+++ b/src/go/internal/gccgoimporter/importer_test.go
@@ -92,6 +92,7 @@
 	{pkgpath: "nointerface", name: "I", want: "type I int"},
 	{pkgpath: "issue29198", name: "FooServer", want: "type FooServer struct{FooServer *FooServer; user string; ctx context.Context}"},
 	{pkgpath: "issue30628", name: "Apple", want: "type Apple struct{hey sync.RWMutex; x int; RQ [517]struct{Count uintptr; NumBytes uintptr; Last uintptr}}"},
+	{pkgpath: "issue31540", name: "S", want: "type S struct{b int; map[Y]Z}"},
 }
 
 func TestGoxImporter(t *testing.T) {
diff --git a/src/go/internal/gccgoimporter/parser.go b/src/go/internal/gccgoimporter/parser.go
index d0081ad..5fd913c 100644
--- a/src/go/internal/gccgoimporter/parser.go
+++ b/src/go/internal/gccgoimporter/parser.go
@@ -31,6 +31,7 @@
 	typeData []string                  // unparsed type data (v3 and later)
 	fixups   []fixupRecord             // fixups to apply at end of parsing
 	initdata InitData                  // package init priority data
+	aliases  map[int]string            // maps saved type number to alias name
 }
 
 // When reading export data it's possible to encounter a defined type
@@ -57,6 +58,7 @@
 	p.scanner = new(scanner.Scanner)
 	p.initScanner(filename, src)
 	p.imports = imports
+	p.aliases = make(map[int]string)
 	p.typeList = make([]types.Type, 1 /* type numbers start at 1 */, 16)
 }
 
@@ -238,17 +240,22 @@
 // Field = Name Type [string] .
 func (p *parser) parseField(pkg *types.Package) (field *types.Var, tag string) {
 	name := p.parseName()
-	typ := p.parseType(pkg)
+	typ, n := p.parseTypeExtended(pkg)
 	anon := false
 	if name == "" {
 		anon = true
-		switch typ := deref(typ).(type) {
-		case *types.Basic:
-			name = typ.Name()
-		case *types.Named:
-			name = typ.Obj().Name()
-		default:
-			p.error("anonymous field expected")
+		// Alias?
+		if aname, ok := p.aliases[n]; ok {
+			name = aname
+		} else {
+			switch typ := deref(typ).(type) {
+			case *types.Basic:
+				name = typ.Name()
+			case *types.Named:
+				name = typ.Obj().Name()
+			default:
+				p.error("anonymous field expected")
+			}
 		}
 	}
 	field = types.NewField(token.NoPos, pkg, name, typ, anon)
@@ -495,6 +502,7 @@
 		}
 		t := p.parseType(pkg, nlist...)
 		obj = types.NewTypeName(token.NoPos, pkg, name, t)
+		p.aliases[nlist[len(nlist)-1]] = name
 		scope.Insert(obj)
 		return t
 	}
@@ -702,7 +710,8 @@
 		if p.tok == scanner.Ident && p.lit == "inl" {
 			return nil
 		}
-		return types.NewTuple(types.NewParam(token.NoPos, pkg, "", p.parseTypeAfterAngle(pkg)))
+		taa, _ := p.parseTypeAfterAngle(pkg)
+		return types.NewTuple(types.NewParam(token.NoPos, pkg, "", taa))
 
 	case '(':
 		params, _ := p.parseParamList(pkg)
@@ -876,16 +885,18 @@
 //
 func (p *parser) parseType(pkg *types.Package, n ...int) types.Type {
 	p.expect('<')
-	return p.parseTypeAfterAngle(pkg, n...)
+	t, _ := p.parseTypeAfterAngle(pkg, n...)
+	return t
 }
 
 // (*parser).Type after reading the "<".
-func (p *parser) parseTypeAfterAngle(pkg *types.Package, n ...int) (t types.Type) {
+func (p *parser) parseTypeAfterAngle(pkg *types.Package, n ...int) (t types.Type, n1 int) {
 	p.expectKeyword("type")
 
+	n1 = 0
 	switch p.tok {
 	case scanner.Int:
-		n1 := p.parseInt()
+		n1 = p.parseInt()
 		if p.tok == '>' {
 			if len(p.typeData) > 0 && p.typeList[n1] == nil {
 				p.parseSavedType(pkg, n1, n)
@@ -908,7 +919,7 @@
 
 	default:
 		p.errorf("expected type number, got %s (%q)", scanner.TokenString(p.tok), p.lit)
-		return nil
+		return nil, 0
 	}
 
 	if t == nil || t == reserved {
@@ -919,6 +930,15 @@
 	return
 }
 
+// parseTypeExtended is identical to parseType, but if the type in
+// question is a saved type, returns the index as well as the type
+// pointer (index returned is zero if we parsed a builtin).
+func (p *parser) parseTypeExtended(pkg *types.Package, n ...int) (t types.Type, n1 int) {
+	p.expect('<')
+	t, n1 = p.parseTypeAfterAngle(pkg, n...)
+	return
+}
+
 // InlineBody = "<inl:NN>" .{NN}
 // Reports whether a body was skipped.
 func (p *parser) skipInlineBody() {
diff --git a/src/go/internal/gccgoimporter/testdata/issue31540.go b/src/go/internal/gccgoimporter/testdata/issue31540.go
new file mode 100644
index 0000000..2c6799e
--- /dev/null
+++ b/src/go/internal/gccgoimporter/testdata/issue31540.go
@@ -0,0 +1,26 @@
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package issue31540
+
+type Y struct {
+	q int
+}
+
+type Z map[int]int
+
+type X = map[Y]Z
+
+type A1 = X
+
+type A2 = A1
+
+type S struct {
+	b int
+	A2
+}
+
+func Hallo() S {
+	return S{}
+}
diff --git a/src/go/internal/gccgoimporter/testdata/issue31540.gox b/src/go/internal/gccgoimporter/testdata/issue31540.gox
new file mode 100644
index 0000000..abdc696
--- /dev/null
+++ b/src/go/internal/gccgoimporter/testdata/issue31540.gox
@@ -0,0 +1,16 @@
+v3;
+package issue31540
+pkgpath issue31540
+types 11 7 23 23 20 22 20 21 57 31 45 36
+type 1 "A1" = <type 4>
+type 2 "A2" = <type 1>
+type 3 "S" <type 7>
+type 4 "X" = <type 8>
+type 5 "Y" <type 9>
+type 6 "Z" <type 10>
+type 7 struct { .go.mapalias.b <type -11>; ? <type 2>; }
+type 8 map [<type 5>] <type 6>
+type 9 struct { .go.mapalias.q <type -11>; }
+type 10 map [<type -11>] <type -11>
+func Hallo () <type 3>
+checksum C3FAF2524A90BC11225EE65D059BF27DFB69134B