By means of an example it is shown that a supercritical bifurcation of an invariant $2$-torus into an invariant $3$-torus prevailing in the case of nonresonance may be replaced by a transcritical bifurcation into a pinched invariant $3$-torus in the case of resonance. The connections of these bifurcation phenomena with the properties of the spectrum of the underlying invariant $2$-torus are discussed.