The thought that it can be efficient to combine two or more multiproduct firms (plants) is made precise by \textit{W. Baumol, J. Panzar} and \textit{R. Willig} [''Contestable markets and the theory of industry structure''; San Diego: Harcourt, Brace, Jovanovich (1982)]. In particular, the notion of economies of scope is introduced to model the gains of combining two or more firms (plants) producing different outputs. One economic importance of economies of scope is stated in Proposition 9.B.1, p. 248, of the above-mentioned book: ''Multiproduct firms in a competitive equilibrium must enjoy (at least weak) economies of scope over the set of products which they produce; that is economies of scope are necessary for the existence of multiproduct competitive firms.'' Various parametric methods have been suggested to test or estimate economies of scope. The purpose of this paper is to introduce a nonparametric (linear programming) approach, along the lines suggested by \textit{S. N. Afriat} [Int. Econ. Rev. 13, 568-598 (1972; Zbl 0264.90022)], \textit{W. E. Diewert} and \textit{C. Parkan} [in: Quant. Studies on Prod. and Prices. Würzburg (1983)], and the author, \textit{S. Grosskopf} and \textit{C. A. K. Lovell} [''The measurement of efficiency of production'', Boston (1985)] to estimate or test economies of scope. The paper unfolds as follows. In Section II a measure à la Farrell is introduced to gauge efficiency gains from combining two or more multiproduct firms (plants). Section III is devoted to developing a nonparametric (linear programming) method for calculating the efficiency gains.