We introduce a class of multivariate dispersion models suitable as error distributions for generalized linear models with multivariate non-normal responses. The models preserve some of the main properties of the multivariate normal distribution, and include the elliptically contoured distributions and certain other known distributions as special cases. We give explicit methods for constructing multivariate proper dispersion models. This is exemplified by constructing multivariate gamma, Laplace, hyperbola, and von Mises distributions.