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A methodological approach for modelling the spatial multivariate distribution of multiple bioclimatic indices is presented. The value of the indices is modelled by means of a Bayesian conditional coregionalised linear model. Elicitation of prior distributions and approximation of posterior distributions of the parameters in the proposed model are also discussed. A posterior predictive distribution and a spatial bioclimatic probability distribution for each bioclimatic index are obtained. This allows researchers to obtain the probability of each location belonging to different bioclimates. The presented methodology is applied in a practical setting showing that the spatial bioclimatic probability distributions are more realistic than the ones obtained in the univariate setting, while providing an interesting tool in the context of climate change.