Considering a set of coupled nonautonomous differential equations with discontinuous righthand sides, we discuss two different scenarios for torus birth bifurcations in piecewisesmooth dynamical systems. One scenario is the continuous transformation of the stable equilibrium into an unstable focus period1 orbit surrounded by a resonant or ergodic torus. Another is the transition from a stable periodic orbit to an invariant torus through a bordercollision bifurcation in which two complexconjugate multipliers jump abruptly from the inside to the outside of the unit circle.
