The nuclear quadrupole coupling constants (e(2)qQ) and asymmetry parameters (eta) for the N-14 nuclei in the beta-HMX molecule are investigated by the Hartree-Fock-Roothaan variational procedure. For the two pairs of equivalent nuclei in the ring positions, the theoretical values are found to be -5.936 and -6.069 MHz for e(2)qQ and 0.432 and 0.490 for eta, which are in good agreement with the corresponding experimentally observed magnitudes of 5.791 and 6.025 MHz for e(2)qQ and the values 0.4977 and 0.5180 for eta obtained from single-crystal measurements by the nuclear quadrupole resonance technique. Possible factors that could further improve the already close quantitative agreement between theory and experiment are also discussed. For the NO2 groups in the peripheral positions the calculated values for e(2)qQ were found to be 1.442 and 1.369 for the two pairs of equivalent N-14 nuclei, substantially smaller than for the ring nuclei, while for eta the corresponding values of 0.553 and 0.571 are close to those for the ring nuclei. Experimental values obtained for the magnitudes of e(2)qQ for N-14 in the NO2 groups are found to be 0.840 and 0.806 MHz, the corresponding eta being 0.42 and 0.48. Reasons for the weaker agreement with experiment, in contrast to the case of ring N-14 nuclei, are suggested, the principal one being the possibility of strong intermolecular bonding between the oxygen ligands of the NO2 groups and hydrogens in neighboring molecules. Calculated values of e(2)qQ and eta for O-17 and H-2 are presented for the beta-HMX molecule with the hope that experimental values will become available for them in future for comparison with theory, allowing one to test whether the intermolecular interactions between oxygen and hydrogen atoms also influence their nuclear quadrupole interaction parameters.