Cell progression through the mitotic cycle during low dose rate irradiation may alter notably the survival probability, particularly when a fraction of the dose is delivered during a sensitive phase of the cycle. In this paper we indicate that the consequences of this phenomenon, commonly believed to lead to an "inverse dose rate effect", may be significantly modulated (and even cancelled) as a result of (a) interactions among sublethal lesions produced in different phases of the mitotic cycle, and (b) variations in these lesions' production rates and repair ability from one phase of the cycle to another. The mathematical model presented (and accompanying numerical examples) takes into account the possibility of changes (e.g. radioactive decay) in the dose rate during exposure.