We apply a generalized Bayesian age–period–cohort (APC) model to a data-set on lung cancer mortality in West Germany, in the period 1952–1996. Our goal is to predict future death rates until the year 2010, separately for males and females. Since age and period are not measured on the same grid, we propose a generalized APC model where consecutive cohort parameters represent strongly overlapping birth cohorts. This approach results in a rather large number of parameters, where standard algorithms for statistical inference by Markov chain Monte Carlo methods turn out to be computationally intensive. We propose a more efficient implementation based on ideas of block sampling from the time series literature. We entertain two different formulations, penalizing either first or second differences of age, period and cohort parameters. To assess the predictive quality of both formulations, we first forecast the rates for the period 1987–1996 based on data until 1986. A comparison with the actual observed rates is made based on a predictive deviance criterion. Predictions of lung cancer mortality until 2010 are then reported and a modification of the formulation in order to include information on cigarette consumption is finally described.