The ASEP (Asymmetric Simple Exclusion Process) model system with two types of particles is studied. The system is interesting because it exhibits spontaneous symmetry breaking when parameters controlling the dynamics of the two types of particles of the same system. By using Mean Field approximation its extended phase diagram was obtained for non-symmetric values of entering rates of the two types of particles. The system is understood to be the combination of two decoupled ASEP systems with one type of particle system for the values of equal hopping and exchange rates. (Evans et al.,PR E, 74 208, (1995)) It is understood that for the exchange rates different from the hopping rates the system can no longer be analyzed as combination of two decoupled one particle ASEP. The “tiny phase” first observed by Evans et al, is examined in more detail. It is found that this phase still exists when entering rates are not symmetric. Also, Monte Carlo simulations for certain values of parameters of the system were carried out to determine the particle density profiles. The phase diagram of the system displays unexpectedly rich structure for the relatively simple dynamics.