We propose a general class of fat-tailed distributions which includes the t,Cauchy, Laplace and slash distributions as well as the normal distribution as spe-cial cases. Full conditional posterior distributions for the Bayesian VAR-model arederived and used to construct a MCMC-sampler for the joint posterior distribution.The framework allows for selection of a specic special case as the distribution forthe error terms in the VAR if the evidence in the data is strong while at the sametime allowing for considerable exibility and more general distributions than oeredby any of the special cases.