Abstract.The density of a d-dimensional polynomial-Gaussian distribution (PGDj)is the product of a non-negative polynomial and a Gaussian density. The density of a (PGDd) has many properties similar to a d-dimensional Gaussian distribution (GDj), but one-dimensional marginal distributions of (PGDj) are (PGDi). Analogously onedimensional densities of a polynomial-Gaussian process (PGP) are (PGD\). We investigate the differences and similarities between the Gaussian and non-Gaussian cases.