This paper presents a multi-vehicle decentralized SLAM algorithm. We expose the different problems involved by this decentralized setting, such as network aspects (data losses, latencies or bandwidth requirements) or data incest (double-counting information), and address them. In order to ease the data association process and also guarantee the consistency of the vehicles localizations, we introduce a new model to represent the natural drift affecting SLAM algorithms. By integrating this model, loop closures, associations between robots and absolute information can be easily taken into account. A general framework has been designed thus allowing to use any SLAM algorithm. To demonstrate the feasibility of our approach, we applied it to a monocular solution. It is the first time, to our knowledge, that a monocular decentralized SLAM is presented. A multi-robot data association algorithm, based on geometric constraints is also exposed in this paper. The validation is performed thanks to a simulator presenting a realistic physics. The results show that the localizations consistency is preserved. It also demonstrates that multi-vehicle monocular SLAM is viable in urban environments.