The behavior of a class of dynamic population models that can be described as a life table operating on a population with a stock recruit relation formed by the product of the egg production and a survival function was examined. A combination of analytical and simulation methods were used to find necessary conditions for the stability of equilibrium populations and the properties of fluctuations about the equilibrium. Regular oscillations that occurred in populations with an unstable equilibrium were of most interest and these were considered as possible causes of the regular fluctuations in populations of fish such as sockeye salmon, Oncorhynchus nerka, or blue pike, Stizostedion vitreum glaucum.