© 2016, Springer Science+Business Media Dordrecht. Usually, the physical interest of the Lorenz system is restricted to the region where its three parameters are positive. However, this famous system appears, when ?< 0 , in the study of a thermosolutal convection model and in the analysis of traveling-wave solutions of the Maxwell–Bloch equations. In this context, a Takens–Bogdanov bifurcation of heteroclinic type becomes an important organizing center. It has been very recently shown that the periodic orbit born in the Hopf bifurcation of the origin undergoes a torus bifurcation. In this paper we perform a detailed numerical study of the resonances of periodic orbits in the three-parameter Lorenz system, x?=?(y-x),y?=?x-y-xz,z?=-bz+xy, when ?< 0 and ?, b> 0. The combination of numerical continuation methods and Poincaré sections of the flow provides important information of how the resonances appear and evolve giving rise to a very rich dynamical and bifurcation scenario.