diff --git a/c++/h5/CMakeLists.txt b/c++/h5/CMakeLists.txt
index 7ba8404f..2832f0d0 100644
--- a/c++/h5/CMakeLists.txt
+++ b/c++/h5/CMakeLists.txt
@@ -57,6 +57,9 @@ target_compile_options(hdf5 INTERFACE ${HDF5_DEFINITIONS})
 if(HDF5_VERSION VERSION_GREATER 1.10)
   target_compile_definitions(hdf5 INTERFACE H5_USE_110_API)
 endif()
+if(HDF5_VERSION VERSION_GREATER_EQUAL 1.13)
+  target_compile_definitions(hdf5 INTERFACE H5_VER_GE_113)
+endif()
 
 # Link against interface target and export
 target_link_libraries(h5_c PRIVATE hdf5)
diff --git a/c++/h5/object.hpp b/c++/h5/object.hpp
index 799eb4a6..9f2330d7 100644
--- a/c++/h5/object.hpp
+++ b/c++/h5/object.hpp
@@ -29,7 +29,12 @@ namespace h5 {
   // Hence complex installation paths to hdf5 are only needed in the cpp file,
   // not by the users of the library.
   using hid_t   = int64_t;
-  using hsize_t = unsigned long long;
+  using hsize_t =
+#ifdef H5_VER_GE_113
+     uint64_t;
+#else
+     unsigned long long;
+#endif
   using v_t     = std::vector<hsize_t>;
 
   // A complex compound type consisting of two doubles