In selecting designs when some of the two-factor interactions are important, the key issues are to permit estimation of the main effects and important twofactor interactions in a postulated model and to minimize the bias caused by the other effects not included in the model. If the main effects need more protection than the important two-factor interactions, we should first minimize the bias of the main effects, and then minimize the bias of the important two-factor interactions. In this paper, a two-stage minimum aberration criterion is proposed to minimize the bias of the main effects and that of the important two-factor interactions sequentially. Searching for the best designs according to this criterion is discussed and some results for designs of 16 and 32 runs are presented.