diff --git a/compiler/src/dotty/tools/dotc/typer/Namer.scala b/compiler/src/dotty/tools/dotc/typer/Namer.scala
index 02607393580d..41917a3ea82f 100644
--- a/compiler/src/dotty/tools/dotc/typer/Namer.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Namer.scala
@@ -888,8 +888,8 @@ class Namer { typer: Typer =>
       val unsafeInfo = if (isDerived) rhsBodyType else abstracted(rhsBodyType)
 
       def opaqueToBounds(info: Type): Type =
-        if sym.isOpaqueAlias && tparamSyms.isEmpty && info.typeParams.nonEmpty then
-          report.error(em"opaque type alias must be fully applied", rhs.srcPos)
+        if sym.isOpaqueAlias && info.typeParams.nonEmpty && info.hkResult.typeParams.nonEmpty then
+          report.error(em"opaque type alias cannot have multiple type parameter lists", rhs.srcPos)
         sym.opaqueToBounds(info, rhs1, tparamSyms)
 
       if (isDerived) sym.info = unsafeInfo
diff --git a/docs/docs/reference/other-new-features/opaques-details.md b/docs/docs/reference/other-new-features/opaques-details.md
index e6021a4a3b9a..ccbbc1770429 100644
--- a/docs/docs/reference/other-new-features/opaques-details.md
+++ b/docs/docs/reference/other-new-features/opaques-details.md
@@ -46,6 +46,20 @@ object o {
 def id(x: o.T): o.T = x
 ```
 
+### Type Parameters of Opaque Types
+
+Opaque type aliases can have a single type parameter list. The following aliases
+are well-formed
+```scala
+opaque type F[T] = (T, T)
+opaque type G = [T] =>> List[T]
+```
+but the following are not:
+```scala
+opaque type BadF[T] = [U] =>> (T, U)
+opaque type BadG = [T] =>> [U] => (T, U)
+```
+
 ### Translation of Equality
 
 Comparing two values of opaque type with `==` or `!=` normally uses universal equality,
diff --git a/tests/neg/i9735.scala b/tests/neg/i9735.scala
new file mode 100644
index 000000000000..a76aad435a00
--- /dev/null
+++ b/tests/neg/i9735.scala
@@ -0,0 +1,12 @@
+trait Two[A, B]
+
+opaque type U[A] = [B] =>> Two[A, B] // error: opaque type alias cannot have multiple type parameter lists // error: cannot instantiate
+opaque type T = [A] =>> [B] =>> String // error: opaque type alias cannot have multiple type parameter lists
+opaque type S = [B] =>> String // ok
+opaque type IArray[+T] = Array[? <: T] // ok
+opaque type S2[B] = String // ok
+
+opaque type BadF[T] = [U] =>> (T, U)    // error
+opaque type BadG = [T] =>> [U] =>> (T, U) // error
+
+