We consider the problem of testing a simple hypothesis: observed sequence of points corresponds to a periodic Poisson process with known intensity against nonparametric alternative. Under alternativie the observations correspond either to a periodic Poissonian process (with a different intensity) or to a self-exciting point process. In both cases we study Cramér-von Mises and Kolmogorov-Smirnov type goodness-of-fit tests. In the case of self-exciting alternatives we equally construct a LAUMP test. The results are illustrated by numerical simulations.