We propose a new model for regression and depen-dence analysis when addressing spatial data with pos-sibly heavy tails and an asymmetric marginal distri-bution. We first propose a stationary process withtmarginals obtained through scale mixing of a Gaus-sian process with an inverse square root process withGammamarginals.Wethengeneralizethisconstructionby considering a skew-Gaussian process, thus obtain-ing a process with skew-t marginal distributions. For theproposed (skew)tprocess, we study the second-orderand geometrical properties and in thetcase, we provideanalytic expressions for the bivariate distribution. In anextensive simulation study, we investigate the use of theweighted pairwise likelihood as a method of estimationfor thetprocess.Moreover we compare the performanceof the optimal linear predictor of thetprocess versus theoptimal Gaussian predictor. Finally, the effectiveness ofour methodology is illustrated by analyzing a georefer-enced dataset on maximum temperatures in Australia
