In this paper, an empirical investigation into parameter variation in diusion models is conducted. Speci®cally, parameter estimates for two consumer durable products are obtained for time-invariant, ¯exible-form and stochastic-parameter speci®cations. Existing diusion models considered in the empirical analysis include the Bass (1969), Easingwood, , and Horsky (1990) diusion models. In addition, a new model is developed that can be estimated with varying parameter structures, and which includes marketingmix variables and replacement sales. In the empirical analysis, three estimation procedures are employed: non-linear least squares, a stationary stochastic procedure (Harvey and Phillips' 1982 `Return to Normality' model using the Kalman ®lter), and a non-stationary stochastic speci®cation (Cooley and Prescott, 1973, 1976). The results suggest that stochastic parameter speci®cations can be easily used to produce substantially better ®ts and that the improvement can be dramatic. Stochastic parameter speci®cations are especially useful in the case of weak priors on the likely pattern of variation. Since some degree of parameter variation is often likely to exist, specifying the exact form of the variation is important, albeit dicult. Stochastic parameter speci®cations can be very helpful in this regard. In addition, tracing the parameter path over time can assist in detecting how current period parameter estimates deviate from the average over this life of the sample.