In many technical systems, the system state, which is to be controlled, is not directly accessible, but has to be estimated from observations. Furthermore, the uncertainties arising from this procedure are typically neglected in the controller. To remedy this deficiency, in this paper, we present a novel approach to stochastic nonlinear model predictive control (NMPC) for heavily noise-affected systems with not directly accessible, i.e., hidden states, extending the stochastic NMPCframework presented in . An important property of our novel method is that, in contrast to classical approaches, time-variant system and measurement equations as well as time-variant step rewards can be considered. Extending the techniques from  by introducing virtual future observations and combining this with a novel tree search algorithm, called probabilistic branch-and-bound search (PBAB), a solution with a feasible computational demand of the challenging problem is possible.