The consensus problem of heterogeneous first-order multi-agent systems with diverse nominal velocities is investigated in this paper, and three adaptive consensus algorithms are constructed by introducing an adaptive variable into the usual consensus algorithm. Under fixed interconnection topology, consensus criteria are obtained for the three algorithms. Moreover, delay-dependent consensus criteria are also presented for the three algorithms in synchronously coupled form under identical input delay and communication delay. Numerical examples are presented to illustrate the validity of our theoretical results.