The general asymptotic theory of parameter estimation for statistical experiments of any nature developed by A. Wald, L. Le Cam, J. Wolfowitz, J. H~ijek, and others is exposed in the monograph of I. A. Ibragimov and R. Z. Hasminskii [1]. In particular, for a family of regular experiments, they establish general conditions assuring the asymptotic efficiency of the maximum likelihood and Bayesian estimators. For concrete statistical experiments, it is important to obtain conditions that can be easily checked. Such conditions are obtained by Yu. A. Kutoyants for Poisson-type processes [4] and for the inmogeneous Poisson process [2, 3], and by Yu. N. Linkov for counting processes, renewal processes, and for semimartingales [5, 6]. In this paper we establish asymptotic properties of the maximum likelihood estimators and Bayesian estimators based on observations of a multivariate point process. In Sect. 1 we introduce the necessary notation from the theory of random processes and the statistical estimation theory. In this section, we also state the main result and prove it in Sect. 2. In Sect. 3 we indicate the changes in the conditions established in Sect. 2 for inhomogeneous Poisson processes and renewal processes.