The authors describe the newly developed diagnostic methods for sex identification based on the step-by-step variant of the Fisher unidimensional (UDA) and multidimentional (MDA) discriminative analysis. The study is based on the materials including the craniometric data (absolute measurements n=87, indicators n=63) characteristic of the main anthropological features of the Russian Caucasian population (691 men and 376 women). Sex diagnostics using the ODA technique performed separately for each trait yielded significant, probable, and uncertain estimates in about 78, 15 and 7% cases of the total, respectively. It was shown that the results obtained with the use of the MDA method allow for the practically significant conclusions in 35.50—67.33% of the cases, probable and uncertain conclusions in 16.47—30.10 and 15.87—34.59% of the cases respectively. The probable conclusions were found to be associated with the erroneous classification in 3.30 to 7.58% of the cases. The application of the ODA method in the combination with MDA guarantees the significant solution of the problem in 85.8 to 92.7% of the cases and practically excludes erroneous diagnostics. The results of verification of the proposed methods based on the results of the measurement of 13 skulls are in excellent agreement with the calculated data.