In this paper we present a synthesis of the work pe rformed on two inference algorithms: the Pearl’s belief propagation (BP) algorithm applied t o Bayesian networks without loops (i.e. polytree) and the Loopy belief propagation (LBP) al gorithm (inspired from the BP) which is applied to networks containing undirected cycles. I t is known that the BP algorithm, applied to Bayesian networks with loops, gives incorrect numerical results i.e. incorrect posterior probabilities. Murphy and al. [7] find that the LBP algorithm converges on several networks and when this occurs, LBP gives a good approximation of the exact posterior probabilities. However this algorithm presents an oscillatory behaviour wh en it is applied to QMR (Quick Medical Reference) network [15]. This phenomenon prevents the LBP algorithm from converging towards a good approximation of posterior probabili ties. We believe that the translation of the inference computation problem from the probabilisti c framework to the possibilistic framework will allow performance improvement of LBP algorithm. We hope that an adaptation of this algorithm to a possibilistic causal network will sh ow an improvement of the convergence of LBP.