Ionizing radiation damage to a mammalian genome is modeled using continuous time Markov chains. Models are given for the initial infliction of DNA double strand breaks by radiation and for the enzymatic processing of this initial damage. Damage processing pathways include DNA double strand break repair and chromosome exchanges. Linear, saturable, or inducible repair is considered, competing kinetically with pairwise interactions of the DNA double strand breaks. As endpoints, both chromosome aberrations and the inability of cells to form clones are analyzed. For the post-irradiation behavior, using the discrete time Markov chain embedded at transitions gives the ultimate distribution of damage more simply than does integrating the Kolmogorov forward equations. In a representative special case explicit expressions for the probability distribution of damage at large times are given in the form used for numerical computations and comparisons with experiments on human lymphocytes. A principle of branching ratios, that late assays can only measure appropriate ratios of repair and interaction functions, not the functions themselves, is derived and discussed.