We present the true second-order theory of the Zeeman effect of the nuclear quadrupole resonance of nuclei with I = 1 with polycrystalline samples. In a previous publication [J. Chem. Phys. 59, 4197 (1973)] an approximation was used and certain deviations were observed when comparing the results with the experimental points. The present theory gives excellent agreement with experiment for practically any nonzero value of the asymmetry parameter and for any value of the angle between the radiofrequency magnetic field and the Zeeman magnetic field. Thus, the results we present are the basis for the method for the identification of lines and the measurement of asymmetry parameters. © 1979.