Résumé : A total of 3 480 K--mesons has been observed. Of these 445 interact in flight, at a mean energy of 40 MeV and only their general characteristics have been studied. Little difference has been observed between the number of unstable charged particles (Σ±-hypersons and π±-mesons) in these interactions and those in the 3 035 interactions at rest. The 3 035 K--interactions at rest have been studied in detail. In this paper (Part I) are given the results on those interactions in which π-mesons are emitted. An estimate of the Σ-hyperon nuclear potential is based on the energy spectrum of π-mesons emitted in the K--interactions in which the only charged particles emitted are a π-meson and a Σ-hyperon. A detailed examination of the angular distribution of 2-pronged events, and of the sign ratio of the π-mesons, the prong distribution and energy release in all events has led to an estimate of the probabilities of absorption of positive and negative Σ-hyperons in the parent nucleus, and to a partition of the events between the various primary reactions. © 1959 Società Italiana di Fisica.