Bayesian modelling for cost-effectiveness data has received much attentionin both the health economics and the statistical literature, in recentyears. Cost-effectiveness data are characterised by a relativelycomplex structure of relationships linking a suitable measure ofclinical benefit (e.g. quality-adjusted life years) and the associatedcosts. Simplifying assumptions, such as (bivariate) normality ofthe underlying distributions, are usually not granted, particularlyfor the cost variable, which is characterised by markedly skeweddistributions. In addition, individual-level data sets are oftencharacterised by the presence of structural zeros in the cost variable.Hurdle models can be used to account for the presence of excess zerosin a distribution and have been applied in the context of cost data.We extend their application to cost-effectiveness data, defininga full Bayesian specification, which consists of a model for theindividual probability of null costs, a marginal model for the costsand a conditional model for the measure of effectiveness (given theobserved costs). We presented the model using a working example todescribe its main features.