We give the double and single logarithmic radiative (order α) corrections to νμe and νμe scattering cross sections for the case of high energy incident neutrinos and high energy recoil electrons scattered in a bubble chamber. We use the exact bremsstrahlung cross section so that both “hard” as well as “soft” photon contributions are included. Logarithmic order α corrections arising in one loop approximation to the Weinberg-Salam theory are also discussed.