Résumé : Kπ scattering is studied in 77 300 bubble chamber events of K+p→K+π-π+p and 18800 events of K+p→Koπoπ+pfor beam momenta between 2.5 and 12.7 GeV/c. The on-shell moments of the angular distribution and the cross sections for K+π-→K+π-, K+π- →K0π0 and K+πo→Koπ+ are obtained by extrapolation to the pion pole. The same procedure applied to the π+p system correctly reproduces the known π+p scattering. A Kπ phase shift analysis between threshold and 1.1 GeV yields two solutions for the S wave isospin 1 2 phase shift (δ01). One solution gives a slowly increasing δ01 which approaches about 70° at 1.1 GeV. The other solution superposes on this behaviour a relatively narrow ({less-than or approximate} 30 MeV) resonant δ01 state near 890 MeV. Either case is compatible with a resonance in δ11 near 895 MeV and with a small, negative δ03. © 1972.