This paper studies the high-order consensus problem for heterogeneous multi-agent systems with unknown communication delays. A necessary and sufficient condition is given for the existence of a high-order consensus solution to heterogeneous multi-agent systems. The condition shows that, for systems with diverse communication delays, high-order consensus does not require the self-delay of each agent to be equal to the corresponding communication delay. When the communication delays are unknown, a simple adaptive adjustment algorithm is presented for on-line adjusting self-delays. (C) 2012 Elsevier Ltd. All rights reserved.