Bayesian networks (BN) constitute a useful tool to model the joint distribution of a set of random variables of interest. To deal with the problem of learning sensible BN models from data, we have previously considered various evolutionary algorithms for searching the space of BN structures directly. In this paper, we explore a simple evolutionary algorithm designed to search the space of BN equivalence classes. We discuss a number of issues arising in this evolutionary context and provide a first assessment of the new class of algorithms.