A nonlinear networked control system is considered in which the measured values are asynchronously sampled and transmitted over multiple communication links. The effects of communication in each link (transmission delay, packet loss and sampling jitter) are captured by a time-varying delay element. A sufficient condition for asymptotic stability of the resulting nonlinear delayed model is provided using the Lyapunov-Krasovskii method. This condition is in the form of a compact linear matrix inequality (LMI) which depends on the amount of communication effects in each link. The results are applied to a robot arm networked control system to show the capabilities of the proposed method. Comparison with the previous works indicates that a considerable improvement in the delay bounds for stability is achieved.