The effect of an external magnetic field on the various possible parametric instabilities of the longitudinal beat wave at the difference frequency of two incident laser beams in a hot plasma has been theoretically investigated. The kinetic equation is employed to obtain the nonlinear response of the magnetized electrons caused by the nonlinear coupling of the beat wave with the low‐frequency electrostatic plasma modes. It is noted that the growth rates of the three‐wave and the four‐wave parametric instabilities can be influenced by the external transverse magnetic field.