Let {Z’ø(t)} be a multitype finite-mean supercritical (CMJ) process with general characteristic ø and malthusian parameter α. It is shown that there exist some constants {c(t)} such that {c’-1(t)Z’ø(t)} converges almost surely to a non-degenerate limit W’ø as t⇒•. Characterizations of {c(t)} and W’ø are also given.
