We have calculated the real part χ ′ of the nonlinear dielectric susceptibility of amorphous in-sulators in the kHz range, by using the two-level system model and a nonperturbative numerical quantum approach. At low temperature { \it T} , it is first shown that the standard two-level model should lead to a decrease of χ ′ when the measuring field E is raised, since raising E increases the population of the upper level and induces Rabi oscillations cancelling the ones induced from the ground level. This predicted E-induced decrease of χ ′ is at odds with experiments. However, a good agreement with low-frequency experimental nonlinear data is achieved if, in our fully quantum simulations, interactions between defects are taken into account by a new relaxation rate whose efficiency increases as $\sqrt E$, as was proposed recently by Burin et al. (Phys. Rev. Lett. 86, 5616 (2001)). In this approach, the behavior of χ ′ at low T is mainly explained by the efficiency of this new relaxation channel. This new relaxation rate could be further tested since it is shown that it should lead: i) to a completely new nonlinear behavior for samples whose thickness is ≃ 10 nm; ii) to a decrease of nonequilibrium effects when E is increased.