The performance of a slow Time Division Multiple Access System (TDMA) for Low Earth Orbiting Spacecraft (LEO) communications through a Data Relay Satellite, is analyzed in this paper and compared with different access systems such as Sequential Access, Code Division Multiple Access (CDMA) and Frequency Division Multiple Access (FDMA). The study shows that such a system for non-real time applications is an interesting and efficient alternative to the classical systems because of the reduced hardware complexity of the Multiple Access payload on the Data Relay Satellite. For real time applications like Hermes audio and video transmission, a dedicated link is envisaged; this link can be reused for LEO ranging and for backup operations. TDMA is also attractive from the flexibility point of view because the user channel throughput can be easily adapted modifying the time slot allocation. The main drawback of such a system is a slightly more complicate modem design and the higher transmitter peak power required on the LEO user to to achieve a given Bit Error Rate.