The generalized fluctuation–dissipation relations that produce the regularized Kappa distributions are studied. The two-variable Fokker–Planck equation, as well as its reductions in the absence of potential and in the overdamped limit, are considered. All these Fokker–Planck equations have the regularized Kappa distributions as the stationary solutions if the friction and diffusion coefficients satisfy the generalized fluctuation–dissipation relations. In addition, we prove that the principle of detailed balance holds for all the stationary solutions derived in this work.