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This paper reports the magnetic characteristics of the oscillation in the axial and transverse magnetic fields derived from the measurements for the oscillation spectra in the 492.4 nm He-Zn II, and in the simultaneously operating 537.8 and 636.0 nm He-Cd II hollow cathode lasers. The simultaneous oscillation in the He-Cd II lasers is compared to the monochromatic one in each wavelength. The experimental data in the magnetic fields are well explained by the theoretical treatment including not only Zeeman effects but also the plasma effects in which the excitation mechanisms are considered using the rate equations. The electron density in the laser plasma that depends on the magnetic fields plays an important role in the excitation mechanisms. This paper proposes that the magnetic characteristics will be used for the color control of a white light laser as well as for the improvement of the monochromaticity in the anomalously broadened lasers.