The breakdown of a radio-frequency discharge excited by a radio-frequency voltage of frequency lying between 7 and 10 Mc/sec has been studied in a cylindrical discharge tube (length 10 cm) in air and in nitrogen with the pressure varying between 10 and 300 μ, in the presence of a nonresonant magnetic field varying from 0 to 80 gauss. The breakdown voltage is found to be greater than when no magnetic field is present for all values of pressure, and the pressure at which the breakdown voltage becomes minimum increases with the application of the magnetic field. Kihara's theory regarding radio-frequency discharge (1952) has been modified by the introduction of effects due to the magnetic field, and a new expression for the breakdown voltage and the pressure at which the breakdown voltage becomes minimum has been deduced. The new expression explains the observed results, and the quantitative disagreement has been ascribed to the uncertainty in the numerical values of the molecular constants introduced by Kihara in his theory. The effect of attachment in the case of air has been calculated within some limitations and it has been observed that when attachment is taken into consideration, the calculated theoretical values are in better agreement with the observed experimental results.