While measuring the ratio R_K = Gamma(K+e2(gamma))/Gamma(K+mu2(gamma)), the KLOE Collaboration has studied the radiative process Ke2gamma. The ratio of the width for the Ke2gamma decay with a positively polarized photon from structure-dependent radiation to the inclusive Kmu2(gamma) width is found to be 1.484(68) 10-5. The observed radiation spectrum agrees with predictions from chiral perturbation theory and is in contrast with predictions based on the light front quark model. This result reduces the contribution to systematic uncertainties on measurements of R_K. In a separate study, KLOE has measured the ratio of the radiative Ke3gamma decay width to the inclusive Ke3(gamma) width to be 924(28) 10-5. The distribution in energy and angle of the radiative photon has been analyzed in an attempt to isolate the signature from interference of the inner-bremsstrahlung and structure-dependent amplitudes.