This paper extends some well known distribution-free structural results in the univariate and multivariate hypothese testing to stochastic processes. The study of distribution-free tests is essentially the study of similar sets and test functions. It is found that (i) all distribution-free statistics are based on permuations through of the basic PITMAN functions; (ii) the optimal tests are based on the likelihoood function of the alternatives; (iii) that a generation of DARMOIS-PITMAN-KOOPMAN families. Furthermore, it is observed that for martingales and MARKOV processes asymptotically optimal tests can be constructed by employing various limit theorems.