The method of calculation of effective vertices of interaction of the Reggeized gluon and quark with particles in QCD in the next-to-leading order is developed. The method is demonstrated in the case of already known vertices of both gluon-gluon and quark-quark transitions in the scattering of gluons and quarks on the Reggeized gluon. It is used for the calculation of the gluon-quark transition in the scattering on the Reggeized quark.