  In a multitype branching process, it is assumed that immigrants arrive
according to a nonhomogeneous Poisson or a generalized Polya process (both
processes are formulated as a nonhomogeneous birth process with an appropriate
choice of transition intensities). We show that the renormalized numbers of
objects of the various types alive at time $t$ for supercritical, critical, and
subcritical cases jointly converge in distribution under those two different
arrival processes. Furthermore, some transient moment analysis when there are
only two types of particles is provided. AMS 2000 subject classifications:
Primary 60J80, 60J85; secondary 60K10, 60K25, 90B15.
