A code based on a set of coupled-rate equations for tandem mirror confinement is used to study two time-dependent phenomena: start-up in the Lawrence Livermore Laboratory Tendem Mirror Experiment (TMX) and alpha-particle build-up in a tandem mirror reactor. The start-up studies indicate that it is possible to achieve near-steady-state conditions in a TMX discharge, provided the sources are suitably programmed. The alpha-particle studies show that build-up of thermalized alphas can seriously degrade the efficiency of a reactor, and that cyclic operation can be used to significantly reduce the degradation.