This paper discusses several Media Access Control (MAC) protocols that will be used in the satellite segment of future mobile communication networks. The scenario is given by Low Earth Orbit-Mobile Satellite Systems (LE-MSSs). Demand-assignment protocols that are evolutions of the classical Packet Reservation Multiple Access (PRMA) scheme are considered. Two types of traffic are addressed: the voice traffic and a bursty data traffic related to Internet surfing. Quality-of-service parameters are used to compare the performance of different MAC schemes. The paper highlights significant tradeoffs involved in the design of satellite MAC protocols.