General solutions are presented in power series form of kinetic equations for the annealing of radiation defects in an elemental semiconductor such as germanium. A kinetic model with an arbitrary number of types of defect complexes is considered, as well as a simple model based on only one species of defect complex. For the simple model, it is shown that a single nonlinear differential equation can be derived for the fraction of defects not annealed. The first integral of this nonlinear equation is obtained for a special case.