Discrimination is considered between two possible sources based on dependent observations of their output. The discrimination problem is modeled by means of a general binary hypothesis test, the main emphasis being on situations that cannot be modeled as signals in additive noise. The observations are modeled as stationary m-dependent or rho -mixing processes. The structure of the discriminator is such that the observations are passed through a memoryless nonlinearity summed up to form a test statistic, which is then compared to a threshold. Only fixed sample size tests are considered. Four different performance measures, which resemble the signal-to-noise ratios encountered in the signal in additive noise problems, are derived under different problem formulations. The optimal nonlinearities for each of the performance measures are derived as solutions to various integral equations. For three of the four performance measures the authors have successfully obtained robust nonlinearities for uncertainty in the marginal and the joint probability density functions of the observations. Computer simulation results that demonstrate the advantage of using these nonlinearities over the i.i.d. nonlinearity under the probability of error criterion are presented.>