We consider the problem of combining belief functions in a situation where pieces of evidence are held by agents at the node of a communication network, and each agent can only exchange information with its neighbors. Using the concept of weight of evidence, we propose distributed implementations of Dempster’s rule and the cautious rule based, respectively, on average and maximum consensus algorithms. We also describe distributed procedures whereby the agents can agree on a frame of discernment and a list of supported hypotheses, thus reducing the amount of data to be exchanged in the network. Finally, we show the feasibility of a robust combination procedure based on a distributed implementation of the random sample consensus (RANSAC) algorithm.