diff --git a/compiler/src/dotty/tools/dotc/core/Definitions.scala b/compiler/src/dotty/tools/dotc/core/Definitions.scala
index 8d305eef16e1..5684dd5a082b 100644
--- a/compiler/src/dotty/tools/dotc/core/Definitions.scala
+++ b/compiler/src/dotty/tools/dotc/core/Definitions.scala
@@ -1430,7 +1430,7 @@ class Definitions {
   )
   private val compiletimePackageBooleanTypes: Set[Name] = Set(tpnme.Not, tpnme.Xor, tpnme.And, tpnme.Or)
   private val compiletimePackageStringTypes: Set[Name] = Set(
-    tpnme.Plus, tpnme.Length, tpnme.Substring, tpnme.Matches, tpnme.CharAt
+    tpnme.Plus, tpnme.Length, tpnme.Substring, tpnme.Matches, tpnme.CharAt, tpnme.LT, tpnme.GT, tpnme.LE, tpnme.GE
   )
   private val compiletimePackageOpTypes: Set[Name] =
     Set(tpnme.S, tpnme.From)
diff --git a/compiler/src/dotty/tools/dotc/core/TypeEval.scala b/compiler/src/dotty/tools/dotc/core/TypeEval.scala
index 98578f353b96..30f00bf2475a 100644
--- a/compiler/src/dotty/tools/dotc/core/TypeEval.scala
+++ b/compiler/src/dotty/tools/dotc/core/TypeEval.scala
@@ -261,6 +261,10 @@ object TypeEval:
               constantFold3(stringValue, intValue, intValue, (s, b, e) => s.substring(b, e))
             case tpnme.CharAt     =>
               constantFold2AB(stringValue, intValue, _.charAt(_))
+            case tpnme.LT         => constantFold2(stringValue, _ < _)
+            case tpnme.GT         => constantFold2(stringValue, _ > _)
+            case tpnme.LE         => constantFold2(stringValue, _ <= _)
+            case tpnme.GE         => constantFold2(stringValue, _ >= _)
             case _ => None
           else if owner == defn.CompiletimeOpsBooleanModuleClass then name match
             case tpnme.Not        => constantFold1(boolValue, x => !x)
diff --git a/library/src/scala/compiletime/ops/string.scala b/library/src/scala/compiletime/ops/string.scala
index 9ef5a3fb7b79..daf08138b10b 100644
--- a/library/src/scala/compiletime/ops/string.scala
+++ b/library/src/scala/compiletime/ops/string.scala
@@ -15,6 +15,50 @@ object string:
    */
   infix type +[X <: String, Y <: String] <: String
 
+  /** Lexicographic comparison of two `String` singleton types.
+   *  ```scala
+   *  //{
+   *  import compiletime.ops.string.*
+   *  //}
+   *  val hello: "hello " < "world" = true
+   *  ```
+   *  @syntax markdown
+   */
+  infix type <[S1 <: String, S2 <: String] <: Boolean
+
+  /** Lexicographic comparison of two `String` singleton types.
+   *  ```scala
+   *  //{
+   *  import compiletime.ops.string.*
+   *  //}
+   *  val hello: "hello " > "world" = false
+   *  ```
+   *  @syntax markdown
+   */
+  infix type >[S1 <: String, S2 <: String] <: Boolean
+
+  /** Lexicographic comparison of two `String` singleton types.
+   *  ```scala
+   *  //{
+   *  import compiletime.ops.string.*
+   *  //}
+   *  val hello: "hello " >= "world" = false
+   *  ```
+   *  @syntax markdown
+   */
+  infix type >=[S1 <: String, S2 <: String] <: Boolean
+
+  /** Lexicographic comparison of two `String` singleton types.
+   *  ```scala
+   *  //{
+   *  import compiletime.ops.string.*
+   *  //}
+   *  val hello: "hello " <= "world" = true
+   *  ```
+   *  @syntax markdown
+   */
+  infix type <=[S1 <: String, S2 <: String] <: Boolean
+
   /** Length of a `String` singleton type.
    *  ```scala
    *  //{
diff --git a/tests/neg/singleton-ops-string.scala b/tests/neg/singleton-ops-string.scala
index c24a9c0e64d1..9b05216ee172 100644
--- a/tests/neg/singleton-ops-string.scala
+++ b/tests/neg/singleton-ops-string.scala
@@ -34,4 +34,66 @@ object Test {
   val t18: CharAt["String", -1] = '?' // error
   //       ^
   //       String index out of range: -1
+
+  val t19: "hello" < "world" = true
+  val t20: "hello" < "world" = false // error
+
+  val t21: "hello" > "world" = false
+  val t22: "hello" > "world" = true // error
+
+  val t23: "hello" <= "world" = true
+  val t24: "hello" <= "world" = false // error
+  val t25: "hello" <= "hello" = true
+  val t26: "hello" <= "hello" = false // error
+
+  val t27: "hello" >= "world" = false
+  val t28: "hello" >= "world" = true // error
+  val t29: "hello" >= "hello" = true
+  val t30: "hello" >= "hello" = false // error
+
+  import scala.compiletime.ops.int./
+
+  type If[C <: Boolean, Then, Else] = C match
+    case true  => Then
+    case false => Else
+
+  type ZipTuples[First, Second] = (First, Second) match
+    case (first *: EmptyTuple, second *: EmptyTuple) => (first, second) *: EmptyTuple
+    case (first *: firstRest, second *: secondRest) => (first, second) *: ZipTuples[firstRest, secondRest]
+
+  type TuplePairs[InputTuple] = InputTuple match
+    case NamedTuple.NamedTuple[names, values] => ZipTuples[names, values]
+
+  type PrependTuplePairs[First, Second, Pairs] = Pairs match
+    case EmptyTuple => (First *: EmptyTuple) *: (Second *: EmptyTuple) *: EmptyTuple
+    case left *: right *: EmptyTuple => (First *: left) *: (Second *: right) *: EmptyTuple
+
+  type UnzipTuples[Input] = Input match
+    case (first *: second *: EmptyTuple) *: rest => PrependTuplePairs[first, second, UnzipTuples[rest]]
+    case EmptyTuple => EmptyTuple
+
+  type NamedTupleFromPairs[Input] = UnzipTuples[Input] match
+    case EmptyTuple => NamedTuple.NamedTuple[EmptyTuple, EmptyTuple]
+    case left *: right *: EmptyTuple => NamedTuple.NamedTuple[left, right]
+
+  type Merge[P1 <: Tuple, P2 <: Tuple] <: Tuple = (P1, P2) match
+    case (EmptyTuple, h *: t) => h *: t
+    case (h *: t, EmptyTuple) => h *: t
+    case ((k1, v1) *: t1, (k2, v2) *: t2) => If[k1 <= k2,
+      (k1, v1) *: Merge[t1, (k2, v2) *: t2],
+      (k2, v2) *: Merge[(k1, v1) *: t1, t2]
+    ]
+
+  type SortPairs[P <: Tuple] <: Tuple = P match
+    case EmptyTuple => EmptyTuple
+    case h *: EmptyTuple => h *: EmptyTuple
+    case _ => Merge[
+      SortPairs[Tuple.Take[P, Tuple.Size[P] / 2]],
+      SortPairs[Tuple.Drop[P, Tuple.Size[P] / 2]]
+    ]
+
+  type SortNamedTuple[NT <: NamedTuple.AnyNamedTuple] = NamedTupleFromPairs[SortPairs[TuplePairs[NT]]]
+
+  val t31: SortNamedTuple[(foo: 45, bar: "x", baz: 6.0, quux: false)] = (bar = "x", baz = 6.0, foo = 45, quux = false)
+  val t32: SortNamedTuple[(foo: 45, bar: "x", baz: 6.0, quux: false)] = (foo = 45, bar = "x", baz = 6.0, quux = false) // error
 }