This paper addresses the problem of probabilistic reasoning as it applies to Truth Maintenance Systems (TMS). A computer-based Belief Maintenance System (BMS) has been constructed which manages a current set of probabilistic beliefs in much the same way that a TMS manages a set of true/false beliefs. It may be thought of as a generalization of a TMS. It enables one to reason using normal two- or three-valued logic or using probabilistic values to represent partial belief. The basic design of the BMS includes three components: (1) conceptual control structure; (2) user hooks to the knowledge base; and (3) an uncertainty calculus. The uncertainty calculus incorporates frames of discernment based on the Dempster-Shafer theory of evidence, but the system could be adapted to other uncertainty models such as Bayesian decision theory. The structure of support links is described along with the control structure which can modify these links. A particular challenge for control structures is the interpretation of circular evidence. Examples of frames of discernment and a probabilistic deductive reasoning sequence are presented. Finally, a rule-based pattern-matching scheme is applied to account for analogies. (Author/LPG)