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This paper presents two new promising rules of combination for the fusion of uncertain and potentially highly conflicting sources of evidences in the framework of the theory of belief functions in order to palliate the well-know limitations of Dempster's rule and to work beyond the limits of applicability of the Dempster-Shafer theory. We present both a new class of adaptive combination rules (ACR) and a new efficient Proportional Conflict Redistribution (PCR) rule allowing to deal with highly conflicting sources for static and dynamic fusion applications., Comment: Presented at Cogis '06 Conference, Paris, March 2006