Abstract. Randic index of a graph G is R(G)=Σ(d_u.d_v)^-1/2, where the sum is taken over all edges uv of G and d_x is the degree of x. Recently it's simplified modification R(G)'=Σ(max{d_u,d_v})^-1, which represents a lower bound for R(G), was found useful. In this paper we introduce generalizations of R' and its counterpart R'' defined as R(G)'_a=Σmin{d_u^a,d_v^a} and R(G)''_a=Σmax{d_u^a,d_v^a} for any real number a. These values bound the Randic index. We study extremal values of R(G)'_a and R(G)''_a in the class of connected graphs and trees.