[en] The decay K⁺→e⁺γγ has been investigated. For the structure-dependent part with positive γ-helicity (SDsub(+)) the branching ratio GAMMA(SDsub(+))/GAMMA(Ksub(μ2)) = (2.33+-0.42) X 10^-5 is obtained from 51+-3 events observed in the kinematical region Esub(e) >= 235 MeV, Esub(γ)>48 MeV and thetasub(eγ)>140⁰. For the corresponding part with negative γ-helicity an upper limit GAMMA(SDsub(-))/GAMMA(SDsub(+))<11 (90% CL) is obtained from the sample of electrons with energies 220 MeV<=Esub(e)<230 MeV and with no γ in the backward direction. This upper limit implies that the ratio of structure-dependent axial vector and vector amplitudes lies outside the region -1.8< asub(K)/γsub(K)<-0.54. For the decay K⁺ →e⁺γγanti γ the limit GAMMA(K⁺→e⁺γγanti γ)/GAMMA(Ksub(e2))<3.8 (90% confidence level) was found. (Auth.)