Since the heterogeneous multi-agent systems composed of first-order and second-order agents have input and velocity saturation characteristics, the systems cannot achieve consensus. A leaderless distributed controller and a leader-following distributed controller of the heterogeneous multi-agent systems were constructed, and the sufficient conditions ensuring the successful consensus were given. The range of communication gain was calculated by using Lyapunov stability theory and Lasalle invariant set principle. The result of numerical simulation of leaderless heterogeneous multi-agent systems with input and velocity saturation characteristics shows that when the communication gain is not in a proper range, consensus of the leaderless heterogeneous multi-agent systems can not be achieved. However, when the proposed gain selection method is used to select the communication gain, the heterogeneous multi-agent systems can overcome input and velocity saturation characteristics, then consensus of the leaderless heterogeneous multi-agent systems can be achieved. The result of numerical simulation of leader following heterogeneous multi-agent systems with input and velocity saturation characteristics proves that the calculation method of the communication gain is also applicable to the semi-global leader-following consensus control of the heterogeneous multi-agent systems.