The static and frequency-dependent hyperpolarizabilities of the N-2 molecule have been calculated using the coupled cluster approximate triples model CC3. The CC3 basis-set limit of the hyperpolarizability has been estimated. Considering the zero-point vibrational correction and neglecting the relativistic contributions (which are found to be small) the best estimate of the static hyperpolarizability is 912.9 +/-4.3 a.u. (the uncertainty of 4.3 a.u. does not account for correlation effects beyond CC3). The effect of triples is important and increases with frequency. The hyperpolarizabilities calculated at the M level agree well with experiment, the discrepancies being of 0.1-2.2%. The largest CC3 calculations employed 326 basis functions. (c) 2005 Elsevier B.V. All rights reserved.