An AQM (active queue management) control algorithm is a complicated dynamical nonlinear feedback system, which is applied at the link node to control the congestion rates based on the network loadings from the source nodes. In order to investigate the influence of the communication delays on the quality of service (QoS) of the Internet, the stability of an AQM algorithm with communication delays is studied by applying the general Nyquist criterion. The stability criteria of the AQM scheme with the homogeneous delays and heterogeneous delays are obtained by analyzing the frequency function of the network system. These results exhibit that the communication delay is one of the key factors to affect the Internet capability and plays an important role in communicating process of the Internet. A computer simulation supports the validity of these stability criteria on the AQM congestion control algorithm.