Rapid eye movement (REM) sleep is a recurring state throughout the sleeping period. Based on the examination of 45 sleep records of 3-mo-old male rats during the middle of the light phase, a stochastic model is proposed for the sequence X(1),Y(2), X(2),Y(2),. of REM sleep durations X and inter-REM sleep waiting times Y experienced by a rat during a sleeping period. In our model the probability distribution of any variable in the sequence, given the past, is allowed to depend on only the immediately previous variable. The conditional distributions f(y(i) | x(i)) and g(x(i+1) | y(i)) do not depend on the index i. It is shown that the marginal distributions tend to stationarity. Aggregations of the data on a discrete time scale suggest that the conditional distributions be formulated as two-component mixtures. These component distributions are modeled as Poisson and their means are called the means of short and long waiting time and the means of short and long REM sleep duration. Associated with each mean is a probability weight. Parametric forms are given to the means and probability weights. The model estimated by maximum likelihood shows a good fit to data of the 3-mo-old rats. The model fit to a smaller data set obtained from rats aged 15-22 mo shows a significant shortening of the means for both short and long REM sleep bout durations compared with the means of the 3-mo-old rats. Neuronal correlates for the behavior of the model are discussed in the context of the reciprocal interaction model of REM sleep regulation.