Аннотация:The main goal of the NA62 experiment at CERN is a study of the ultra rare decay K→πvv¯. The collected statistics allows to analyse other rare decays, in particular, K+ → μ+vμ+μ−. Rare decays make it possible to experimentally investigate one of the aspects of the Standard Model, the chiral perturbative theory (ChPT). ChPT predicts decay probability of K+ → μ+vμ+μ−: 1.35 х 10−8. This decay channel is also of great interest due to the fact, that it was not experimentally observed, there is only an upper limit < 4.1 х 10−7 CL 90%. We present the research methodology, the first results of signal selection and the study of the background sources for the decay.