A problem encountered in the econometric estimation of dynamic models of livestock systems is dynamic instability during simulation of models. In the case of systems where economic decisions are involved in the breeding and the slaughter of animals it is possible for parameters to be obtained which generate dynamic instability. In the paper, a simple representation of the dynamics of a livestock system is examined using techniques of dynamic analysis. The dynamic stability of such models depends fundamentally on the parameters determining the births and deaths and thus the relative flows in and out of the stock of animals. In some situations very narrow stability ranges for the values of the parameters are observed.