This paper addresses the stability-analysis problem for teleoperation systems with time delays. Compared with previous work, communication delays are assumed to be both time-varying and asymmetric, which is the case for network-based teleoperation systems. The stability analysis is performed for two classes of controllers: delayed position-error feedback and delayed torque feedback. By choosing Lyapunov-Krasovskii functional, we show that the master-slave teleoperation system is stable under specific linear-matrix-inequality (LMI) conditions. With the given controller-design parameters, the proposed stability criteria can be used to compute the allowable maximal transmission delay. Finally, both simulations and experiments are performed to show the effectiveness of the proposed method.