We introduce two subclasses T ∗(p, α, j) and C(p, α, j) (0 ≤ α < p − j + 1, 1 ≤ j ≤ p, p ∈ 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 c...