The basic goal of this study is to determine the relationship between the fatigue damage predicted for Gaussian and nongaussian processes when both are analyzed by the rainflow counting method. Due to a lack of references on nongaussian process simulation, some initial effort is devoted to finding a simple way of generating nongaussian processes. In this study, in addition to mean and variance (the usual two parameters of a normal distribution), kurtosis is chosen as a third parameter to indicate the degree of non-normality. A theoretical prediction of the fatigue damage due to a nongaussian process is also obtained for the special situation of a narrow-band process with the exponent in the S-N curve limited to integer values. The effect of non-normality on the empirical rainflow results (for any bandwidth process) is shown to be approximately the same as the effect predicted theoretically for the corresponding narrow-band process. A practical example associated with the fatigue life design of an offshore platform is given. It incorporates non-normality considerations into the design procedure. It is concluded that the effect of non-normality should not be neglected. It is also noted that the influence of nonnormality is affected not only by the kurtosis of the stress process, but also by the slope of the S-N curve (which is a material property).