This document provides probabilistic-mechanistic models for describing the cell kill (K) and cell sub-lethal damage (SL) for one fraction with a dose of radiation that is absorbed by a living tissue; also this provides the K and SL formalisms for fractioned irradiation regimens. These models and formalisms are based on real mean behavior of cell survival (S) - a complement of K- and strong probabilistic-radiobiological foundations. The K and SL formalisms include all possible factors affecting the biological radiation effects: dose (d), fractionations (n), SL, and the temporal factors: cell repair and cell repopulation. It is discussed some aspects about the widely used linear-quadratic (LQ) S(d) model and LQ S(n,d) formalism, and one of its derivations, the BED (biologically effective dose). The SMp K(d) parameters can be obtained from S data, or using graphical/analytical tools developed by this study. These new formalisms will be useful for simulations of treatments, and together regional damage distribution for optimizations of the treatment planning.

BED, LQ model, stochastic effects, cell survival