In order to describe the life-prolonging effect of some agents that ar
e harmful at higher doses, ionizing radiations in particular, a stocha
stic model is developed in terms of accumulation and progression of in
tracellular lesions caused by the environment and by the agent itself.
The processes of lesion repair, operating at the molecular and cellul
ar level, are assumed to be responsible for this hormesis effect withi
n the framework of the proposed model. Properties of lifetime distribu
tions, derived for analysis of animal experiments with prolonged and a
cute irradiation, are given special attention. The model provides effi
cient means of interpreting experimental findings, as evidenced by its
application to analysis of some published data on the hormetic effect
s of prolonged irradiation and of procaine on animal longevity.