Let AA be the class of functions f(z)f(z) which are analytic in the open unit disk UU with f(0)=0f(0)=0 and f′(0)=1f′(0)=1. For the class AA, a new general class AkAk is defined. With this general class AkAk, two interesting classes S∗k(α)Sk∗(α) and Kk(α)Kk(α) concerning classes of starlike of order αα in UU and convex of order αα in UU are considered.