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In most empirical work on the market model, the parameters of that model are estimated by ordinary least squares, effectively assuming that the systematic risk of an asset, or portfolio, is constant through time. However, a plausible alternative hypothesis would allow the systematic risk of the stock of a company to vary through time. Such variation may arise through the influence of either microeconomic factors (such as operational changes in the company, or changes in the business environment peculiar to the company), or macroeconomic factors (such as the rate of inflation, general business conditions, and expectations about relevant future events). A detailed discussion of these points is provided by Rosenberg and Guy (1976a, 1976b). Support for the hypothesis that systematic risk varies through time is provided in the studies by Jacob (1971), Blume (1975), and Fabozzi and Francis (1978). In this paper we allow the possibility that systematic risk of an asset is stochastic. In principle, an attempt to model this stochastic behavior could be made through allowing systematic risk to follow a member of the general ARIMA class of models of Box and Jenkins (1970). Ideally, the available data would be employed to suggest a specific model from this general class. However, this approach has to face very serious We discuss the market model in which the possibility is allowed that beta is stochastic and obeys a first-order autoregressive process. Following a brief discussion of methodological issues in the estimation and testing of such models, results are reported on an empirical study of a large sample of monthly returns of common stock. We find strong evidence indicating stochastic systematic risk, but relatively little evidence against the random coefficient model.