Résumé : The final states corresponding to the reaction K+p → KNπππ are studied at 5.0 GeV/c incident momentum. The general characteristics of these reactions are given. A more detailed study is made of resonance production. The more abundantly produced resonances are K*(892), Δ(1236), ρ{variant}, ω, η, K*(1420), N*(1520) and N*(1700). Fits to the multidimensional space of effective masses show that for the final state Kopπ+π-π-, more than 30% of the reaction proceeds through quasi two-body intermediate states, and that more than 88% proceeds through the production of at least one resonance. Some evidence is found for the production of other resonances such as K*(1660) → K3π, Δ(1920) → → pπ+π+π- and N*(2064) → pπ+π-πo. Several example of cascade decays are found, but no direct decay into more than three bodies is observed. © 1973.