  In this paper we extend a result of Dubouloz on the Cancellation Problem in
higher dimensions ($\geqslant 2$) over the field of complex numbers to fields
of arbitrary characteristic. We then apply the generalised result to describe
the Makar-Limanov and Derksen invariant of generalised Asanuma varieties under
certain hypotheses. We also establish a necessary and sufficient condition for
certain generalised Asanuma varieties to be isomorphic to polynomial rings.
