This volume contains the Proceedings of the 1996 Prague Conference on Distributions with Given Marginals and Moment Problems. It provides researchers with difficult theoretical problems that have direct consequences for applications outside mathematics. Contributions centre around the following two main themes. Firstly, an attempt is made to construct a probability distribution, or at least prove its existence, with a given support and with some additional inner stochastic property defined typically either by moments or by marginal distributions. Secondly, the geometrical and topological structures of the set of probability distributions generated by such a property are studied, mostly with the aim to propose a procedure that would result in a stochastic model with some optimal properties within the set of probability distributions. Topics that are dealt with include moment problems and their applications, marginal problems and stochastic order, copulas, measure theoretic approach, applications in stochastic programming and artificial intelligence, and optimization in marginal problems.