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We consider models for spatio-temporal processes which assume either non-negative values, and often are observed as zero, or discrete values and are also inflated by zeros. Typically, in the first case, the spatial observations are obtained at fixed locations (point-referenced data) over a region D; whereas in the second, the region D is divided into a finite number of regular or irregular subregions (areal level), resulting in observations for each subregion. Our main idea is based on those of zeroinflated models, by assuming that the value observed at location s and time t, Y_t (s), is a realization of a mixture between a Bernoulli distribution with a probability of success θ_t (s) and a probability density function or probability function p(y_t (s) | .) For both cases, we include spatio-temporal latent processes in the model to account for the possible extra variation present in the mean structure of θ_t (s …