Some of the ideas arising in queueing theory are applied to describe the repair mechanisms responsible for recovery of cells from potentially lethal radiation damage. Two alternative versions are presented of a queueing model of damage repair after a single dose of irradiation. The first version represents a linear misrepair model, and the second invokes the idea of spontaneous lesion fixation. They are pieced together in the third model, allowing for both mechanisms. The consistency of the proposed models with published experimental data is tested.