We have carried out nonlinear ion conductivity measurements on the supercooled ionic liquid 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide[C6mim][NTf2] by applying ac electric fields with amplitudes up to about 200 kV/cm. At these field amplitudes, 3ω and 5ω harmonic components in the current response were detected, and the higher-order conductivity coefficients σ 3 1, σ 3 3, σ 5 3, and σ 5 5 were determined. The frequency and temperature dependence of these conductivity coefficients was analyzed in detail. The most important findings were the following: (i) The third-order spectra σ 3 1 and σ 3 3 exhibit very similar values in the dc plateau regime but differ considerably in the dispersive regime. The same was observed for the fifth order spectra σ 5 3 and σ 5 5. (ii) In the dispersive regime, the third-order spectra display a minimum, while the fifth-order spectra display a maximum. (iii) The frequencies of these minima and maxima are thermally activated with the same activation energy as the low-field dc conductivity σ1,dc, whereas the dc values of the higher-order conductivity coefficients, σ3,dc and σ5,dc, are characterized by lower activation energies.