Résumé : The cross sections for the reactions: (a) K+p → K+pπ+π-π+ and (b) K+p → K+π+π+π-n have been determined at 8.2 and 16 GeV/c with the following results:. at 8.2 GeV/c: (a) 0.99 ± 0.07 mb, (b) 0.41 ± 0.04 mb;. at 16 GeV/c: (a) 0.72 ± 0.05 mb, (b) 0.28 ± 0.05 mb. Using the available data at other energies, the cross-section dependence of these reactions on the incident momentum is discussed. © 1976.