diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,6 @@
+# 0.6.1 [2023.02.27]
+* Support `th-abstraction-0.5.*`.
+
 # 0.6 [2022.07.03]
 * Loosen the `Monad` constraint in the `Invariant(2)` instances for
   `Kleisli` to an `Invariant` constraint.
diff --git a/invariant.cabal b/invariant.cabal
--- a/invariant.cabal
+++ b/invariant.cabal
@@ -1,5 +1,5 @@
 name:                invariant
-version:             0.6
+version:             0.6.1
 synopsis:            Haskell98 invariant functors
 description:         Haskell98 invariant functors (also known as exponential functors).
                      .
@@ -28,8 +28,10 @@
                    , GHC == 8.6.5
                    , GHC == 8.8.4
                    , GHC == 8.10.7
-                   , GHC == 9.0.1
-                   , GHC == 9.2.1
+                   , GHC == 9.0.2
+                   , GHC == 9.2.6
+                   , GHC == 9.4.4
+                   , GHC == 9.6.1
 extra-source-files:  CHANGELOG.md, README.md
 
 source-repository head
@@ -54,8 +56,8 @@
                      , StateVar             >= 1.1    && < 2
                      , stm                  >= 2.2    && < 3
                      , tagged               >= 0.7.3  && < 1
-                     , template-haskell     >= 2.4    && < 2.19
-                     , th-abstraction       >= 0.4    && < 0.5
+                     , template-haskell     >= 2.4    && < 2.21
+                     , th-abstraction       >= 0.4    && < 0.6
                      , transformers         >= 0.2    && < 0.7
                      , transformers-compat  >= 0.3    && < 1
                      , unordered-containers >= 0.2.4  && < 0.3
@@ -75,7 +77,7 @@
                      , hspec            >= 1.8
                      , invariant
                      , QuickCheck       >= 2.11 && < 3
-                     , template-haskell >= 2.4  && < 2.19
+                     , template-haskell
   build-tool-depends:  hspec-discover:hspec-discover
   ghc-options:         -Wall
   if impl(ghc >= 8.6)
diff --git a/src/Data/Functor/Invariant/TH.hs b/src/Data/Functor/Invariant/TH.hs
--- a/src/Data/Functor/Invariant/TH.hs
+++ b/src/Data/Functor/Invariant/TH.hs
@@ -40,7 +40,7 @@
 import qualified Data.Map as Map ((!), fromList, keys, lookup, member, size)
 import           Data.Maybe
 
-import           Language.Haskell.TH.Datatype
+import           Language.Haskell.TH.Datatype as Datatype
 import           Language.Haskell.TH.Datatype.TyVarBndr
 import           Language.Haskell.TH.Lib
 import           Language.Haskell.TH.Ppr
@@ -510,14 +510,17 @@
           map (substNamesWithKindStar (List.union droppedKindVarNames kvNames'))
             $ take remainingLength varTysOrig
 
-        isDataFamily :: Bool
-        isDataFamily = case variant of
-                         Datatype        -> False
-                         Newtype         -> False
-                         DataInstance    -> True
-                         NewtypeInstance -> True
+    isDataFamily <-
+      case variant of
+        Datatype        -> return False
+        Newtype         -> return False
+        DataInstance    -> return True
+        NewtypeInstance -> return True
+#if MIN_VERSION_th_abstraction(0,5,0)
+        Datatype.TypeData -> typeDataError tyConName
+#endif
 
-        remainingTysOrigSubst' :: [Type]
+    let remainingTysOrigSubst' :: [Type]
         -- See Note [Kind signatures in derived instances] for an explanation
         -- of the isDataFamily check.
         remainingTysOrigSubst' =
@@ -699,6 +702,17 @@
 etaReductionError instanceType = fail $
     "Cannot eta-reduce to an instance of form \n\tinstance (...) => "
     ++ pprint instanceType
+
+#if MIN_VERSION_th_abstraction(0,5,0)
+-- | We cannot implement class methods at the term level for @type data@
+-- declarations, which only exist at the type level.
+typeDataError :: Name -> Q a
+typeDataError dataName = fail
+  . showString "Cannot derive instance for ‘"
+  . showString (nameBase dataName)
+  . showString "‘, which is a ‘type data‘ declaration"
+  $ ""
+#endif
 
 -------------------------------------------------------------------------------
 -- Generic traversal for functor-like deriving