By use of the mechanistic state vector model (MSV model) it is demonstrated that under circumstances where cell division during irradiation is unlikely: 1. A cell survival curve (dose-log surviving fraction curve) that is exponential can be obtained even though some of the surviving cells may have nonlethal damage. Exponential survival curves are said to have zero curvature. 2. In some cases, in the absence of a mixed population, the slope of a single-dose survival curve may decrease in magnitude, as the dose increases for a range of doses. These curves are said to show negative curvature for that range of doses. Fractionating the dose or decreasing the dose rate may result in enhanced cell killing. 3. The initial slope of a mammalian cell survival curve should be independent of the dose rate and number of dose fractions provided that the number of cells having lethal damage builds up to a steady level during the post irradiation time regime. The magnitude of the initial slope will depend on properties of the cells and on properties of the radiation. 4. A nonzero initial slope in the cell survival curve, after exposure to low linear energy transfer (LET) radiation, may be due to biology, rather than physics.