We present several results concerning the construction of the Cramér-von Mises and Kolmogorov-Smirnov type goodness-of-fit tests for inhomogeneous Poisson process. Under the basic hypothesis, the observed process is inhomogeneous Poisson with discontinuous intensity function For this model, we propose tests which are asymptotically distribution-free and consistent. The results of numerical simulations of the tests are presented.
