The conditions whereby the helical instability can excite higher modes in the plasma column are investigated. As the amplitude of the helical instability increases it changes the radial distribution of the averaged charge density. The finite amplitude theory of the helical or m = 1 instability is employed to determine the averaged charged density which is then used to determine the conditions for the onset of the m = 2 instability. The onset of the m = 2 instability is thus determined as a function of the amplitude of the helical instability for specified conditions within the plasma column. These results are then combined with the energy balance relationship of the positive column. The wavelengths and frequencies of the helical and m = 2 modes are determined for the conditions at the onset of the m = 2 mode. The wavelength of the m = 2 mode is found to be shorter than for the helical mode whereas the frequency is found to be greater. (Author).