  In this paper we study some cohomological properties of non-standard
multigraded modules and Veronese transforms of them. Among others numerical
characters, we study the generalized depth of a module and we see that it is
invariant by taking a Veronese transform. We prove some vanishing theorems for
the local cohomology modules of a multigraded module; as a corollary of these
results we get that the depth of a Veronese module is asymptotically constant.
