In this talk I will present a recent result obtained together with Paulo D. Cordaro and Gerson Petronilho, where we give a partial answer to a conjecture made by F. Treves in 1981, concerning the hypoellipticity of corank one locally integrable structures. Besides hypoellipticity, we also consider the same regularity problem for Gevrey classes, and regular Denjoy-Carleman, which includes quasi-analytic classes.