A mixed quantum-classical description of nonadiabatic photoreactions such as internal conversion and electron transfer is outlined. In particular the validity and limitations of Tully's surface-hopping (SH) model [J. Chem. Phys. 93, 1061 (1990)] is investigated in the case of photoinduced relaxation processes which are triggered by a multidimensional conical intersection (or avoided crossing) of two potential-energy surfaces. Detailed numerical studies are presented, adopting (i) a three-mode model of the S-2 --> S-1 internal-conversion process in pyrazine, (ii) a multimode model of ultrafast intramolecular electron-transfer, (iii) a model exhibiting nonadiabatic photoisomerization dynamics, and (iv) various spin-boson-type models with an Ohmic bath for the description of electron-transfer in solution. The SH simulations are compared to exact quantum-mechanical calculations as well as to results obtained by an alternative mixed quantum-classical description, that is, the self-consistent classical-path method. In all cases, the SH data are shown to reproduce the quantum results at least qualitatively; in some cases the SH results are in quantitative agreement with the complex electronic arid vibrational relaxation dynamics exhibited by the quantum calculations. Depending on the physical situation under consideration, either the SH or the self-consistent classical-path method was found to be superior. The characteristic features of a mixed quantum-classical. description of photoinduced bound-state dynamics (e.g., the start of the trajectories on a diabatic electronic potential-energy surface, high chance of a trajectory undergoing multiple electronic transitions) as well as the specific problems of the SH approach are discussed in some detail. In particular, the focus is on the ability of a method to account for the branching of trajectories, to correctly describe the electronic phase coherence and the vibrational motion on coupled potential-energy surfaces, and to obey the principle of microreversibility. Furthermore, an alternative way to handle classically forbidden electronic transitions is proposed, which is shown to lead to significantly better results than the usual procedure. (C) 1997 American Institute of Physics.