Abstract: With the development of computer technology, network technology and communication technology, it is deeply promoted for the modeling and application of the multi-agent systems including the alignment control of unmanned air vehicles (UAVs), the distribution control of the sensor network, and the pose control of the satellite. Recently, there are more and more researchers to bend their minds to study the dynamical alignment control of the multi-agent systems. In this paper, flocking movement of mobile multi-agents system with heterogeneous communication delays and heterogeneous input delays is studied. Suppose the multi-agent systems consist of n agents and a leader, there is a static directed interconnected graph with leader as a globally reachable node. By applying the generalized Nyquist criterion of the frequency domain, the consensus algorithm with heterogeneous communication delays and heterogeneous input delays is analyzed. By utilizing the Greshgorins disc theorem and curvature theory, the flocking motion of delayed multiple-agent algorithm with leader-following is studied, and a decentralized consensus convergence condition is obtained to ensure the flocking movement of the multi-agent systems. This consensus condition applies the local information of every agent, which is dependent on input delays but independent of communication delays. Finally, computer simulation is used to show the validity of the results.