The present invention concerns a plant for the conversion of an olefinic C.sub.4 or C.sub.5 cut to an alkyl-tertiobutylether or alkyl-tertioamylether and to propylene, by metathesis. The plant comprises four successive stages: (1) selective hydrogenation of the diolefins with simultaneous isomerisation of the alpha olefins to internal olefins; (2) etherification of the isoolefins; (3) elimination of oxygen-containing impurities; (4) metathesis of internal olefins with ethylene. Application to C.sub.4 and C.sub.5 steam cracking units.