The focus of this dissertation is the performance analyses of two classes of frequency-hopped spread-spectrum multiple access (FH-SSMA) systems in various fading environments. The capacity of Viterbi's FH-SSMA system is evaluated under three types of fading, namely Rician, shadowed Rician, and Nakagami fading. The results of recent experiments have indicated that these fading phenomena occur in various environments where the FH-SSMA system may be implemented. In this dissertation, the deletion probability for each fading scenario is derived. Subsequently, the system capacity is analyzed in terms of maximum number of users versus average bit error rate. The effect of a change in the signal-to-noise ratio level on the system capacity is also demonstrated. For Rician fading, it is found that the capacity of the system with a Rician factor of 2 dBis reduced by 13 percent as compared to the capacity of the non-fading case. For shadowed Rician fading, three shadowing scenarios are considered: light, average, and heavy. It is shown that the light and the average shadowing scenarios provide only a slight decrease in the capacity, while the heavy shadowing scenario renders a capacity identical to that for the Rayleigh fading case. Finally, for Nakagami fading the capacity is found to decrease by 50 percent as the fading parameter is reduced to 0.5. The performance of a cellular frequency-hopped spread-spectrum multiple access system is studied under an indoor environment. It is demonstrated how the system capacity, given in terms of the number of users per cell, is affected by the number of cells in the system. Also, the influence of the delay spread, which is the result of multipath propagation, is investigated. The analysis focuses on a worst-case scenario where a user receives both the desired and interfering signals with equal power levels. This scenario applies to both the downlink and the uplink. It is shown that the system capacity is reduced drastically as the number of adjacent interfering cells increases from one to three. Previous work concerning the indoor multipath propagation assumed that the number of paths is fixed, the path delays are uniformly distributed, and the path gains are equal. In this dissertation, a more realistic channel model derived from actual impulse response measurements by Saleh and Valenzuela is employed. The model consists of clusters of rays with constant cluster and ray arrival rates and power-delay time constants. The system performance is shown to be affected strongly by the change in the power-delaytime constants, yet only slightly influenced by the variation in the arrival rates of the rays and clusters. In addition, the degradation in the system performance due to the delay spread becomes more severe as the transmission rate increases.