Many applications require computational systems to respond to queries by a particular deadline. Failure to meet the deadlines may render the returned solution useless. Moreover, the deadlines of such time-critical applications are often uncertain at system design time. Anytime algorithms have been suggested to cope with these challenges by trading the quality of the solutions for the reactiveness of the systems at run time [ 13. We have introduced an anytime evaluation algorithm  for a formalism commonly used in uncertain reasoning: Bayesian networks. Empirical results indicate that approximations of good quality can be obtained within a much shorter time than would be required to directly evaluate the networks by exact algorithms. Also the quality of the approximation improves with the allocated computational time on average.