The mathematical models for predicting the updata channel signal- to-noise ratio for the Apollo communications system are developed. The models developed are for hoth ideal phase modulation and for phase modulation with incidental amplitude modulation on the subcarriers . It is shown that incidental amplitude modulation on one subcarrier can degrade the performance of other channels in the system. Predictions are made using the ideal and the nonideal models, and the results are compared to measured results. In addition, some possible solutions to the problem of reducing the effect of incidental amplitude modulation are discussed.