diff --git a/compiler/compiler.go b/compiler/compiler.go
index efbdbccd..f14193a8 100644
--- a/compiler/compiler.go
+++ b/compiler/compiler.go
@@ -3054,7 +3054,7 @@ func (c *Compiler) parseBinOp(op token.Token, typ types.Type, x, y llvm.Value) (
 		} else if typ.Info()&types.IsFloat != 0 {
 			// Operations on floats
 			switch op {
-			case token.ADD:
+			case token.ADD: // +
 				return c.builder.CreateFAdd(x, y, ""), nil
 			case token.SUB: // -
 				return c.builder.CreateFSub(x, y, ""), nil
@@ -3102,14 +3102,23 @@ func (c *Compiler) parseBinOp(op token.Token, typ types.Type, x, y llvm.Value) (
 		} else if typ.Info()&types.IsString != 0 {
 			// Operations on strings
 			switch op {
-			case token.ADD:
+			case token.ADD: // +
 				return c.createRuntimeCall("stringConcat", []llvm.Value{x, y}, ""), nil
-			case token.EQL, token.NEQ: // ==, !=
+			case token.EQL: // ==
+				return c.createRuntimeCall("stringEqual", []llvm.Value{x, y}, ""), nil
+			case token.NEQ: // !=
 				result := c.createRuntimeCall("stringEqual", []llvm.Value{x, y}, "")
-				if op == token.NEQ {
-					result = c.builder.CreateNot(result, "")
-				}
-				return result, nil
+				return c.builder.CreateNot(result, ""), nil
+			case token.LSS: // <
+				return c.createRuntimeCall("stringLess", []llvm.Value{x, y}, ""), nil
+			case token.LEQ: // <=
+				result := c.createRuntimeCall("stringLess", []llvm.Value{y, x}, "")
+				return c.builder.CreateNot(result, ""), nil
+			case token.GTR: // >
+				result := c.createRuntimeCall("stringLess", []llvm.Value{x, y}, "")
+				return c.builder.CreateNot(result, ""), nil
+			case token.GEQ: // >=
+				return c.createRuntimeCall("stringLess", []llvm.Value{y, x}, ""), nil
 			default:
 				return llvm.Value{}, errors.New("todo: binop on string: " + op.String())
 			}
diff --git a/src/runtime/string.go b/src/runtime/string.go
index 540c6410..f3e42df7 100644
--- a/src/runtime/string.go
+++ b/src/runtime/string.go
@@ -32,6 +32,24 @@ func stringEqual(x, y string) bool {
 	return true
 }
 
+// Return true iff x < y.
+//go:nobounds
+func stringLess(x, y string) bool {
+	l := len(x)
+	if m := len(y); m < l {
+		l = m
+	}
+	for i := 0; i < l; i++ {
+		if x[i] < y[i] {
+			return true
+		}
+		if x[i] > y[i] {
+			return false
+		}
+	}
+	return len(x) < len(y)
+}
+
 // Add two strings together.
 func stringConcat(x, y _string) _string {
 	if x.length == 0 {
diff --git a/testdata/binop.go b/testdata/binop.go
index 5526d13b..24774aad 100644
--- a/testdata/binop.go
+++ b/testdata/binop.go
@@ -1,13 +1,30 @@
 package main
 
 func main() {
-	// string equality
+	println("string equality")
 	println(a == "a")
 	println(a == "b")
 	println(a != "a")
 	println(a != "b")
+	println("string inequality")
+	println(a > "b")
+	println("b" > a)
+	println("b" > "b")
+	println(a <= "b")
+	println("b" <= a)
+	println("b" <= "b")
+	println(a > "b")
+	println("b" > a)
+	println("b" > "b")
+	println(a <= "b")
+	println("b" <= a)
+	println("b" <= "b")
+	println(a < "aa")
+	println("aa" < a)
+	println("ab" < "aa")
+	println("aa" < "ab")
 
-	// struct equality
+	println("struct equality")
 	println(s1 == Struct1{3, true})
 	println(s1 == Struct1{4, true})
 	println(s1 == Struct1{3, false})
@@ -17,7 +34,7 @@ func main() {
 	println(s1 != Struct1{3, false})
 	println(s1 != Struct1{4, false})
 
-	// blank fields in structs
+	println("blank fields in structs")
 	println(s2 == Struct2{"foo", 0.0, 5})
 	println(s2 == Struct2{"foo", 0.0, 7})
 	println(s2 == Struct2{"foo", 1.0, 5})
diff --git a/testdata/binop.txt b/testdata/binop.txt
index ef3bec46..1e2f40e7 100644
--- a/testdata/binop.txt
+++ b/testdata/binop.txt
@@ -1,7 +1,26 @@
+string equality
 true
 false
 false
 true
+string inequality
+false
+true
+false
+true
+false
+true
+false
+true
+false
+true
+false
+true
+true
+false
+false
+true
+struct equality
 true
 false
 false
@@ -10,6 +29,7 @@ false
 true
 true
 true
+blank fields in structs
 true
 false
 true