In the case of NMR, nuclei with spin ≥ 1/2 have a magnetic dipole moment so that their energies are split by a magnetic field, allowing resonance absorption of energy related to the Larmor frequency:
where  is the gyromagnetic ratio and  is the (normally applied) magnetic field external to the nucleus.
In the case of NQR, nuclei with spin ≥ 1, such as N, O, Cl and Cu, also have an electric quadrupole moment. The nuclear quadrupole moment is associated with non-spherical nuclear charge distributions. As such it is a measure of the degree to which the nuclear charge distribution deviates from that of a sphere; that is, the prolate or oblate shape of the nucleus.  NQR is a direct observation of the interaction of the quadrupole moment with the local electric field gradient (EFG) created by the electronic structure of its environment. The NQR transition frequencies are proportional to the product of the electric quadrupole moment of the nucleus and a measure of the strength of the local EFG: 
where q is related to the largest principal component of the EFG tensor at the nucleus.  is referred to as the quadrupole coupling constant.
In principle, the NQR experimenter could apply a specified EFG in order to influence  just as the NMR experimenter is free to choose the Larmor frequency by adjusting the magnetic field.  However, in solids, the strength of the EFG is many kV/m^2, making the application of EFG's for NQR in the manner that external magnetic fields are chosen for NMR impractical.  Consequently, the NQR spectrum of a substance is specific to the substance - and NQR spectrum is a so called "chemical fingerprint." Because NQR frequencies are not chosen by the experimenter, they can be difficult to find making NQR a technically difficult technique to carry out. Since NQR is done in an environment without a static (or DC) magnetic field, it is sometimes called "zero field NMR". Many NQR transition frequencies depend strongly upon temperature.