The reactions of K-p → K-p and K-p → KNπ have been studied at 24 momenta between 777 and 1226 MeV/c. For this purpose about 71 000 two-prong events were analyzed, from photographs taken in the 81 cm Saclay hydrogen bubble chamber, exposed to a separated K- beam at the CERN proton synchrotron. Presented here are the partial and differential K-p → K-p cross sections together with a detailed description of the experimental procedure adopted in their determination. The analysis of resonance formation in K-p → KK previously reported has been updated using these new K-p → K-p data. Cross sections for K-p → K-pπ0, K-nπ+, K0pπ- are also given. The analysis of resonance production and formation for these channels will, however, be reported elsewhere. © 1968.