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Consensus problems were investigated for discrete-time heterogeneous multi-agent systems composed of first-order agents and second-order agents. Distributed consensus protocols with and without the bound communication delay were respectively designed. By transforming the systems into autonomous discrete-time linear time-invariant systems and using the matrix theory and algebraic graph theory,sufficient conditions are derived for the systems reaching consensus. The obtained sufficient conditions are related to the sampling period,the control parameter and the system topology structure. It is proved that the consensus of the systems is independent of the bound communication delay. Simulation results verify the correctness of the theoretical results.