Carl said:
There isn't.
Nor is there any replacement for OLE (on which AX controls are built).
If you need to interact with the OLE clipboard, with OLE documents, etc,
you'll be deal with OLE one way or another. Note that you can embed windows
forms controls in web pages, but that requires that the user already has the
.NET framework installed (which many still do not), and that under the
covers it's still an AX control, with .NET providing an elaborate .NET <->
OLE conversion layer to make things work.
I am not familiar with its implementation, but since .NET provides a way
to embed .NET controls in web pages, one should concentrate in these new
stuff and not the old one, since the current technology will keep
supported in WinFX, while the old one probably not.
The same is the case of .NET today, much of its API is implemented by
using Win32 (because there is no reason to create new low level
primitives of similar functionality), however the upcoming API is WinFX
and will be developed independently from Win32 whose development is ceased.
Some parts of it may remain developed by Win32, but the newest parts
will be developed stand alone.
In summary, an application developer should concentrate on the new .NET
functionality.