The convergence and stability analysis for two end-to-end rate-based congestion control algorithms with unavoidable random loss in packets are presented,which can be caused by,for example,errors on wireless links. The convergence rates of these two algorithms are analyzed by linearizing them around their equilibrium points, since they are globally stable and can converge to their unique equilibrium points.Some sufficient conditions for local stability in the presence of round-trip delay are obtained based on the general Nyquist criterion of stability. The stability conditions can be considered to be more general.If random loss in the first congestion control algorithm is not considered,they reduce to the local stability conditions which have been obtained in some literatures. Furthermore,sufficient conditions for local stability of a new congestion control algorithm have also been obtained if random loss is not considered in the second congestion control algorithm. The convergence and stability analysis for two end-to-end rate-based congestion control algorithms with unavoidable random loss in packets are presented, which can be caused by, for example, errors on wireless links. The convergence rates of these two algorithms by linearizing them around their equilibrium points, where they are globally stable and can converge to their unique equilibrium points. Some sufficient conditions for local stability in the presence of round-trip delay are obtained based on the general Nyquist criterion of stability. The stability conditions can be considered to be more general. If you lose to the first congestion control algorithm is not considered, they reduce to the local stability conditions which have been obtained in some literatures. also got obtained if random loss is not considered in the second congestion control algorithm.