A new model of low-frequency fluctuations, based on the thermionic current model [Mathematical Handbook for Scientists and Engineers, New York, 1961; Introduction to Statistical Radio-Physic. Part 1: Random Processes, Moscow, 1976 (in Russian)], has been designed. The proposed model provides calculation of realization, auto-correlation function (ACF) and power spectral density (PSD) of an m-level quantum signal. This model has allowed to explain the reason of very small magnitude of low-frequency (LF) boundary (10(-4) to 10(-2) Hz) on experimental spectra of LF current fluctuations in a metal thermionic cathodes. (C) 2003 Published by Elsevier Science B.V.