||We will survey some recent results on estimating the intensity function of a cyclic Poisson process. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that a nonparametric kernel type estimator of the intensity function of the cyclic Poisson process is consistent, when the size of the window expands. We also compute the asymptotic bias, variance and the mean-squared error of our estimator. Next, we consider the problem to estimate a cyclic Poisson intensity function in the presence of linear trend. For this slightly more complicated situation a new kernel type estimator of the cyclic part is proposed and investigated in detail. This joint work with R. Helmers (CWI, Amsterdam) and R. Zitikis (UWO, London Ont., Canada).