This paper investigates the Centralized Multi-vehicle Simultaneous Localization and Mapping (CMSLAM) problem in the context of the nonlinear observability. Theory is first developed for the nonlinear observability of CMSLAM using the relatively simple unicycle vehicle model, which gives rise to a CMSLAM problem in control affine form. Conditions required for nonlinear observability of CMSLAM when estimating 1. One landmark and 2. More than one landmark are detailed. The theory developed is then extended for more practical car-like vehicle models. CMSLAM simulations and experiments are demonstrated showing the effects of nonlinear observability.