  Let (Z n) n$\ge$0 with Z n = (Z n (i, j)) 1$\le$i,j$\le$p be a p multi-type
critical branching process in random environment, and let M n be the
expectation of Z n given a fixed environment. We prove theorems on convergence
in distribution of sequences of branching processes Zn |Mn| /|Z n | > 0 and ln
Zn $\sqrt$ n /|Z n | > 0. These theorems extend similar results for single-type
critical branching process in random environment.
