In this paper we will discuss two problems related to action recognition: The first problem is the one of identifying in a
surveillance scenario whether a person is walking or running and in what rough direction. The second problem is concerned with the recovery of action primitives from observed complex actions. Both problems will be discussed within a statistical framework. Bayesian propagation over time offers a framework to treat likelihood observations at each time step and the dynamics between the time steps in a unified manner. The first problem will be approached as a patter recognition and tracking task by a Bayesian propagation of the likelihoods. The latter problem will be 
approached by explicitly specifying the dynamics while the likelihood measure will give a measure how good each dynamical model fit at each time step. Extensive experimental results show the applicability of the Bayesian framework for action recognition and round up our discussion.