In this paper, multi-stage RLS algorithm for (CARMA) and the multi-stage RLS algorithm for (CARAR) systems are derived with the intention of estimating the system’s parameters, furthermore, enhance the computation’s efficiency. Decomposing (CARMA) and (CARAR) systems into three subsystems is the fundamental concept, one of that includes one parameter vector, and to identify each subsystem parameters individually. These suggested algorithms exhibit high computational efficiency due to the reduction in the dimensions of their covariance matrices. In conclusion, a simulation example is presented in order to support the Comparison between these two proposed algorithms in terms of accuracy.