The dynamics of Cl(P-2) atoms in a solid Ar matrix is studied, with emphasis on electronic energy relaxation of excited states, and on p-orbital reorientation effects. The method used follows Tully’s approach for nonadiabatic molecular dynamics simulations, which treats the electronic degrees of freedom quantum-mechanically, and the atomic motions classically, allowing for "hopping" of the atoms between different potential energy surfaces. We introduce an extended version of this method, to handle "Berry Phase" effects due to the doubly degenerate Kramers pairs of states present in this system. The role of both electrostatic and of spin-orbit interactions between different electronic states is incorporated in the treatment. The simulations yield a time scale of 13 ps for the energy relaxation of the highest excited electronic state of Cl(P-2). A time scale of similar magnitude is found for the depolarization of this state. However, the time scale for orbital reorientation at thermal conditions is only 0.7 ps. This is attributed to the fact that at thermal conditions, only the two lowest electronic states are populated. The physical mechanisms of these basic radiationless decay processes are discussed on the basis of the simulations.