The present review is the last work published by Leonid Grigor’evich Landsberg (1930-2005). Questions and comments concerning the article are to be addressed to the Editorial Board (e-mail: ufn@ufn.ru).

Feasible searches for anomalous processes involving New Physics in rare decays of K-mesons are considered. Discussed are searches for lepton flavor nonconservation in kaon decays, searches for anomalous scalar, pseudoscalar, and tensor interactions, and searches for nonstandard pro- cesses violating T- (or CP-) invariance in the decays of charged K-mesons. Considered also are searches for new light particles (the P-sgoldstino) in kaon decays and studies involving tagged’ π⁰-mesons produced in K⁰_L→ 3π⁰ and K⁺→ π⁺π⁰ decays, as well as a number of other phenomena. The prospects of future experiments in this field being carried out at new experimental facilities are discussed.