This paper studies a variant of axioms originally developed by Shafer and Shenoy (Shafer and Shenoy, 1988). It is investigated which extra assumptions are needed to perform the local computations in a HUGIN-like architecture (Jensen et al., 1990) or in the architecture of Lauritzen and Spiegelhalter (Lauritzen and Spiegelhalter, 1988). In particular it is shown that propagation of belief functions can be performed in these architectures.