During last decade, smart homes in which the activities of the residents are monitored automatically have been developed and demonstrated. However, smart homes with multiple residents still remains an open challenge. In order to tackle the multiple resident concurrent activity recognition problem in smart homes equipped with interaction-based sensors and with multiple residents, we propose two different approaches. In the first approach, we use a factorial hidden Markov model for modeling two separate chains corresponding to two residents. Secondly, we use nonlinear Bayesian tracking for decomposing the observation space into the number of residents. As opposed to the previous studies, we handle multiple residents at the same time without assuming any explicit identification mechanisms. We perform two experiments on real-world multi-resident Activity Recognition with Ambient Sensing data sets. In each experiment, we compare the proposed approach with a counterpart method. We also compare each approach with the manually separated observation performances. We show that both of the proposed methods consistently outperform their counterparts in both houses of the data sets and for both residents. We also discuss the advantages and disadvantages of each approach in terms of run time complexity, flexibility and generalizability.