We have studied theoretically the magnetoconductance oscillations in a quasi-one-dimensional electron gas with a parabolic transverse confining potential. The solution to Schrödinger's equation is that of a hybrid harmonic oscillator with a frequency that depends on both the parabolic potential and the magnetic field B. At B=0, equals the classical oscillation frequency of the parabolic potential. In the high-field limit, approaches the cyclotron frequency. The result is a nonlinear fan plot for the magnetoconductance minima, which should help to clarify the origin of conductance oscillations in narrow-channel metal-oxide-semiconductor field-effect transistors. © 1986 The American Physical Society.