This paper describes a new theoretical model for the response of cells to radiation. This model is based on the existence of a lesion interaction mechanism in the cell, along with processes of recovery and repair that are able to repair the damage produced by radiation in the cells. Such a mechanism makes the cells evolve from a sublethal state to a normal one. Repair and recovery are not instantaneous, but are produced over an average period that we suppose is represented by an exponential function. The probability of cellular recovery and repair is also affected by radiation. These mechanisms become less probable as the dose administered to the cell increases (repair saturation mechanism). This model is suitable for instantaneous doses as well as for arbitrary dose rates. Results obtained from the model for normal tissues and low doses are approximately equal to those obtained by the linear-quadratic model or by the incomplete repair model. The model yields a survival curve with an exponential tail for high doses and for long periods of irradiation.