We consider deterministic evolutionary dynamics under imitative revision protocols. We allow agents to have different aspiration levels in the imitative protocols where their aspiration levels are not observable to other agents. We show that the distribution of strategies becomes statistically independent of the aspiration level eventually in the long run. Thus, long-run properties of homogeneous imitative dynamics hold as well, despite heterogeneity in aspiration levels. (c) 2014 Elsevier Inc. All rights reserved.