It is well known that a bounded operator with dense range has a nontrivial invariant subspace if and only if its Aluthge transform does. Recently, R. Curto and Jasang Yoon have introduced the toral and spherical Aluthge transforms for commuting pairs and studied their basic properties. In this talk, we talk about nontrivial common invariant subspaces between the toral (resp. spherical) Aluthge transform and the original n-tuple of bounded operators with dense ranges.