We discuss the semiclassical approaches for describing systems with spin-orbit interactions by Flynn (1991, 1992), Frisk and Guhr (1993), and by Keppeler (1998, 1999). We use these methods to derive trace formulae for several two-and three-dimensional model systems, and exhibit their successes and limitations. We discuss, in particular, also the mode conversion problem that arises in the strong-coupling limit.v3, in print for J. Phys. A 35, 6009 (2002) Awhere T ppo is the period of the primitive orbit and M po the stability matrix of the periodic orbit.Examples of amplitude factors for systems with continuous symmetries or for integrable systems may be found in the literature quoted in the introduction. The po sum in (4) does not converge in most cases; it must in general be understood as a an asymptotic series that is only semiconvergent. However, much practical use can be made of trace formulae if one does not attempt to obtain an exact energy spectrum (given by the poles of the