Let Fm(var G) = Lm/I(G) be the relatively free Lie algebra of rank m in the variety of Lie algebras generated by a Lie algebra G over a field K of characteristic 0. We describe the groups of inner and outer automorphisms of the free metabelian nilpotent of class c algebra Lm/(L'' m + Lc+1 m) and the inner automorphisms of the relatively free algebra of rank 2 in the variety varsl2(K) ? n{fraktur}c. To obtain the results we first describe the group of inner automorphisms of the completion of the relatively free Lie algebras Lm/L'' m and F2(varsl2(K)) with respect to the formal power series topology. In the metabelian case we describe also the group of continuous outer automorphisms of the completion
