2000 Mathematics Subject Classification: primary 60J80; secondary 60J85, 92C37.Two-type reducible age-dependent branching processes with inhomogeneous immigration are considered to describe the kinetics of renewing cell populations. This class of processes can be used to model the generation of oligodendrocytes in the central nervous system in vivo or the kinetics of leukemia cells. The asymptotic behavior of the first and second moments, including the correlation, of the process is investigated.This research was supported by NIH grants 2R01 NS039511, R01 CA134839, and 1R01 AI069351
