A semiclassical time-dependent self-consistent-held (TDSCF) formulation is developed for the description of internal conversion (IC) processes in polyatomic molecules. The total density operator is approximated by a semiclassical ansatz, which couples the electronic degrees of freedom to the nuclear degrees of freedom in a self-consistent manner, whereby the vibrational density operator is described in terms of Gaussian wave packets. The resulting TDSCF formulation represents a generalization of familiar classical-path theories, and is particularly useful to make contact to quantum-mechanical formulations. To avoid problems associated with spurious phase factors, we assume rapid randomization of the nuclear phases and a single vibrational density operator for all electronic states. Classically, the latter approximation corresponds to a single trajectory propagating along a "mean path" instead of several state-specific trajectories, which may become a critical assumption for the description of IC processes. The validity and the Limitations of the mean-path approximation are discussed in detail, including both theoretical as well as numerical studies. It is shown that for constant diabatic coupling elements V-kk’ the mean-path approximation should be appropriate in many cases, whereas in the case of coordinate-dependent coupling V-kk’(X) the approximation is found to lead to an underestimation of the overall relaxation rate. As a remedy for this inadequacy of the mean-path approximation, we employ dynamical corrections to the off-diagonal elements of the electronic density operator, as has been suggested by Meyer and Miller [J. Chem. Phys. 70, 3214 (1979)]. We present detailed numerical studies, adopting (i) a two-state three-mode model of the S-1-S-2 conical intersection in pyrazine, and (ii) a three-state five-mode and a five-state sixteen-mode model of the ($) over tilde C-->($) over tilde B-->($) over tilde X IC process in the benzene cation. The comparison with exact basis-set calculations for the two smaller model systems and the possible predictions for larger systems demonstrate the capability of the semiclassical model for the description of ultrafast IC processes.