Nonhomologous end joining (NHEJ) is a major pathway in multicellular eukaryotes for repairing double-strand DNA breaks (DSBs). Here, the NHEJ reactions have been reconstituted in vitro by using purified Ku, DNA-PK(cs), Artemis, and XRCC4:DNA ligase IV proteins to join incompatible ends to yield diverse junctions. Purified DNA polymerase (pol) X family members (pol mu, pol lambda, and TdT, but not pol beta) contribute to junctional additions in ways that are consistent with corresponding data from genetic knockout mice. The pol lambda and pol mu contributions require their BRCT domains and are both physically and functionally dependent on Ku. This indicates a specific biochemical function for Ku in NHEJ at incompatible DNA ends. The XRCC4:DNA ligase IV complex is able to ligate one strand that has only minimal base pairing with the antiparallel strand. This important aspect of the ligation leads to an iterative strand-processing model for the steps of NHEJ.