The one-electron properties and the components of the polarizability tensor of the nitrogen molecule are calculated as functions of internuclear distance using both SCF and CI wavefunctions. The one-electron properties considered are the quadrupole and hexadecapole moments, the electric field gradient at the nitrogen nucleus and the diamagnetic contributions to the magnetizability and the nuclear magnetic shielding constants. The derivatives of these properties and their dependences upon vibrational quantum number are calculated. The CI values of the one-electron properties are compared in detail with the available experimental data, with particular regard to the accuracy of the methods of determining the multipole moments. The CI results for the polarizability and its derivatives are in excellent agreement with experimental data; however there are serious deficiencies in the SCF results and the results of studies on other molecules suggests that this may generally be the case.