Nonlinear dielectric effect (NDE) describes changes of dielectric permittivity induced by a strong electric field in a liquid dielectric. The most classical finding related to this magnitude is the negative sign of NDE in liquid diethyl ether (DEE), recalled by Peter Debye in his Nobel Prize lecture. This article shows that the positive sign of NDE in DEE is also possible, in the supercritical domain. Moreover, NDE on approaching the gas-liquid critical point exhibits a unique critical effect described by the critical exponent ψ ≈ 0.4 close to critical temperature (T(C)) and ψ ≈ 0.6 remote from T(C). This can be linked to the emergence of the mean-field behavior in the immediate vicinity of T(C), contrary to the typical pattern observed for critical phenomena. The multi-frequency mode of NDE measurements made it possible to estimate the evolution of lifetime of critical fluctuations. The new way of data analysis made it possible to describe the critical effect without a knowledge of the non-critical background contribution in prior.