A structure with two periodicities can couple up to six modes under a case of simultaneous resonance resulting in a stop-band interaction. The method of multiple scales is employed to analyze the modal coupling in a two-dimensional acoustic duct with rigid periodically undulated walls as well as in an elastic plate having periodically corrugated outerfaces, leading to the coupled-mode equations. The comparison between the three possible cases of interaction under simultaneous resonance are given in terms of the power reflection coefficient spectrum as a function of frequency. The strength of the stop-band interaction is found to be strongly related to the number of direct couplings between the incident and reflected modes.