Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)In this work we establish new results about the existence of smooth, explicit families of periodic traveling waves for the modified and fourth-order Benjamin-Bona-Mahony equations. We also prove, under certain conditions, that these families are nonlinearly stable in the energy space. The techniques employed may be of further use in the study of the stability of periodic traveling-wave solutions of other nonlinear evolution equations.303851871Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)University of Cordoba, Monteria, ColombiaConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [14/2009]