Summary: For second-order multi-agent systems with exogenous disturbances, a new type of disturbance observers is presented. Under the condition that only a part of agents have access to the information of the reference model, the problems of model-reference consensus for second-order multi-agent systems with exogenous disturbances generated by different exogenous systems are studied. For the cases that the exogenous systems are linear and nonlinear, linear disturbance observers and nonlinear disturbance observers are designed, respectively. Furthermore, the distributed consensus protocol is presented, which can inhibit the disturbance effectively. As a result, the multi-agent systems can achieve consensus with any given reference model. Two examples are provided to illustrate the effectiveness of the proposed methods.