Abstract: Let X be a metric space with metric d, denote the family of all nonempty compact subsets of X and, given , let be the Hausdorff excess of F over G. The excess variation of a multifunction , which generalizes the ordinary variation V of single-valued functions, is defined by where the supremum is taken over all partitions of the interval . The main result of the paper is the following selection theorem: If , , and , then there exists a single-valued function of bounded variation such that for all , , and . We exhibit examples showing that the conclusions in this theorem are sharp, and that it produces new selections of bounded variation as compared with [V.V. Chistyakov, Selections of bounded variation, J. Appl. Anal. 10 (1) (2004) 1–82]. In contrast to this, a multifunction F satisfying for some constant and all with (Lipschitz continuity with respect to ) admits a Lipschitz selection with a Lipschitz constant not exceeding C if and may have only discontinuous selections of bounded variation if . The same situation holds for continuous selections of when it is excess continuous in the sense that as for all and as for all simultaneously. [Copyright &y& Elsevier]