The continuous gamma-ray spectra (inner bremsstrahlung) accompanying orbital electron capture in Ni59, A37, and Fe55 have been studied with the use of a scintillation spectrometer of NaI(Tl). The shape of the spectrum of Ni59 has been found to correspond to a second forbidden spectrum (∆I=2, No) and is distinctly different from that of an allowed one. The parameter, λ, of the correction factor, C2s,T, is approximately 0.33; the value of AijTij, for a pure tensor interaction, is (-6). The probability of emission of a photon of energy greater than 100 kev has been shown to be 1.4+/-0.4 times the theoretical value. The spectrum of A37 has an allowed shape at energies as low as ~35 kev, and the ratio of emission probabilities P(exp)P(theoret) is 1.05+/-0.25 for the region of energy lying above 35 kev. The spectrum of Fe55 has been compared with the calculations of Glauber and Martin. In this case, the value of P(exp)P(theoret) is 1.1+/-0.3 at higher energies.