  The aim of this paper is to introduce a multitype branching process with
random migration following the research initiated with the Galton-Watson
process with migration introduced in [Yanev & Mitov (1980) C. R. Acad. Bulg.
Sci. 33(4):473-475]. We focus our attention in what we call the critical case.
Sufficient conditions are provided for the process to have unlimited growth or
not. Furthermore, using suitable normalizing sequences, we study the asymptotic
distribution of the process. Finally, we obtain a Feller-type diffusion
approximation.
