Slotted ALOHA is proposed as a multiple access scheme for high capacity voice cellular communications in mobile radio environment. The performance of such a system, in the presence of fading and shadowing, is evaluated for both mobile-to-base and base-to-mobile links, in terms of number of supported conversations per cell, under some constraints on maximum tolerable delay. The numerical results show that a system of this sort can compete with other multiaccess schemes currently considered, such as TDMA, FDMA, and even CDMA. A heuristic stability analysis is also presented, showing that the proposed system does not suffer from instability problems. >