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This paper presents new methods for generation of random Bayesian networks. Such methods can be used to test inference and learning algorithms for Bayesian networks, and to obtain insights on average properties of such networks. Any method that generates Bayesian networks must first generate directed acyclic graphs (the "structure" of the network) and then, for the generated graph, conditional probability distributions. No algorithm in the literature currently offers guarantees concerning the distribution of generated Bayesian networks. Using tools from the theory of Markov chains, we propose algorithms that can generate uniformly distributed samples of directed acyclic graphs. We introduce methods for the uniform generation of multi-connected and singly-connected networks for a given number of nodes; constraints on node degree and number of arcs can be easily imposed. After a directed acyclic graphis uniformly generated, the conditional distributions are produced by sampling Dirichlet distributions.