From accurate ab initio calculations in hierarchies of basis sets and wavefunction models, the non-relativistic CCSD(T) basis set limit value of the equilibrium molecular electric quadrupole moment (Theta(e)) of N-2 has been determined, including estimates of the small effects of relativity and correlation beyond CCSD(T), the value obtained is Theta(e) = (-4.99 +/- 0.03) X 10(-4u) Cm-2. The corresponding rovibrationally averaged value Theta(e) = (-4.99 +/- 0.03) X 10(-4u) Cm-2 is in disagreement with the recent experimental value of ( - 4.65 +/- 0.08) X 10(-40) Cm-2. The latter, however, is deduced from the measured effective Theta via a correction term, whose value is questionable. Using a more accurate value for the correction term we obtain the improved experimentally based value (-5.01 +/- 0.08)X 10(-40) Cm-2, which is in good agreement with our theoretical value. (C) 1998 Elsevier Science B.V. All rights reserved.