The classic method for the determination of the electron temperatures t_3,O, t_2,O and t_2,N from forbidden lines of the ions O⁺⁺, O⁺ and N⁺ was considered. The influence of uncertainties in atomic data on the accuracy of the electron temperatures determination was studied. The uncertaities in atomic data (in the Einstein coefficients for spontaneous transitions and in effective collision strengths for electron impacts) were estimated as a discrepancy between some values computed by various authors. It was found that the error in the electron temperature due to uncertainties in the atomic data increased with electron temperature. At a temperature of 10000 K, the error in the electron temperature t_3,O is less than 1 %, the error in the electron temperature t_2,N is not in excess of 3 %, and the error in the electron temperature t_2,O can be as large as 7 %.