The nonlinear absorption of a strong electromagnetic wave caused by electrons confined in cylindrical quantum wires is theoretically studied by using the quantum kinetic equation for electrons. An analytic expression of the nonlinear absorption coefficient of a strong electromagnetic wave caused by electrons confined in a cylindrical quantum wire with a parabolic potential for electron-optical phonon scattering is obtained. The dependence of the nonlinear absorption coefficient on the intensity

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... E 0 and the frequency Ω of the external strong electromagnetic wave, the temperature T of the system and the radius R of the wires is strong and nonlinear. Analytic expression is numerically calculated and discussed for a GaAs/GaAsAl quantum wire. The results are compared with those for normal bulk semiconductors and quantum wells to show the differences.