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

Multitype branching process with nonhomogeneous Poisson and generalized Polya immigration