The Norton–Bass (NB) model is often credited as the pioneering multigeneration diffusion model in marketing. However, as acknowledged by the authors, when counting the number of adopters who substitute an old product generation with a new generation, the NB model does not differentiate those who have already adopted the old generation from those who have not. In this study, we develop a generalized Norton–Bass (GNB) model that separates the two different types of substitutions. The GNB model provides closed-form expressions for both the number of units in use and the adoption rate, and offers greater flexibility in parameter estimation, forecasting, and revenue projection. An appealing aspect of the GNB model is that it uses exactly the same set of parameters as the NB model and is mathematically consistent with the later. Empirical results show that the GNB model delivers better overall performance than previous models both in terms of model fit and forecasting performance. The analyses also show that differentiating leapfrogging and switching adoptions based on the GNB model can help gain additional insights into the process of multigeneration diffusion. Furthermore, we demonstrate that the GNB model can incorporate the effect of marketing mix variables on the speed of diffusion for all product generations.