Abstract: We provide a large toolbox for the construction of non-parametric priors on the survival function of a multivariate random vector. In essence, we assume that the survival function of the random vector can be expressed in terms of a so-called exponent measure, which is assumed to be infinitely divisible. This framework embeds many well-known non-parametric priors on cumulative hazard rates. The posterior distribution of the infinitely divisible exponent measure is derived and shown to exhibit certain conjugacy properties. Since the posterior distribution is not easily interpreted, we provide a construction scheme for a flexible class of priors, which allows to construct new prior distributions from simple building blocks and allows for a closed form posterior representation.