Let A be the class of functions f(z), which are analytic in the unit disc U = {z:\z\ < 1}, with f(0) = f'(0) - 1 = 0. In this paper we introduce a new subclass Q(alpha)(beta) of se and study some properties of Q(alpha)(beta) Hence we extend the results of MacGregor, Chen, and Chichra. We also get a new univalent criterion and some interesting properties of Hadamard products. (C) 1995 Academic Press, Inc.