In this paper we study solutions of the quasi-linear parabolic equations @u=@t pu = a(x)jujq1u in (0; T) with Robin boundary condition @u=@ jrujp2 = b(x)jujr1u in (0; T) @ where is a regular bounded domain in IRN, N 3, q > 1, r > 1 and p 2. Some su cient conditions on a and b are obtained for those solutions to be bounded or blowing up at a nite time. Next we give the asymptotic behavior of the solution in special cases.