Certain moments of the output of a bandpass nonlinear system whose input is a stationary Gaussian random process will be used to evaluate the performance (i.e., the average probability of error) of the system. The main application of this procedure is the analysis of a frequency translating saturating satellite link. The basic analytical technique to be employed will be the use of moment space bounds, it will be shown that by using at most a two-dimensional Gaussian quadrature formula to perform a numerical integration, the bounding procedure presented in this paper can be used in a relatively straightforward manner with virtually any bounded bandpass nonlinearity. Numerical results Corresponding to a hard limiter with only an AM/AM characteristic will be presented, as well as results corresponding to a soft limiter with both AM/AM and AM/PM characteristics. In the latter model, the effects of intersymbol interference will also be included. However, computationally, the procedure is only feasible for a small number of interfering terms.