We introduce two subclasses T * ( p , α, j ) and C ( p , α, j ) (0 £ α < p – j + 1, 1 £ j £ p , p Î N = {1, 2,...}) of p -valent starlike and p -valent convex functions with negative coefficents. In this paper we obtain coefficient inequalities, distortion theorems, extreme points and integral operators for functions belonging to the classes T * ( p , α, j ) and C ( p , α, j ). We also determine the radii of close-to-convexity and convexity for the functions belonging to the class T * ( p , α, j ). Also we obtain several results for the modified Hadamard products of functions belonging to the classes T * ( p , α, j ) and C ( p , α, j ).