New anisotropic potential energy surfaces of the Hartree-Fock plus damped dispersion (HFD) type have been obtained for the N2-Ne and N2-Ar interactions. The SCF energies utilized in constructing the short-range part of the interactions were computed at 20 points on each surface by using basis sets of double zeta plus polarization quality. Anisotropic C 6 and Cs dispersion coefficients, utilized in constructing the long-range part of the interaction, have been calculated with a recently obtained combining rule. Several procedures are introduced for estimating the anisotropic damping factors used in the description of the correlation energy contributions in the HFD model. The essential differences amongst the surfaces reported here arise from these estimates. Comparisons are made with other available anisotropic N2-Ne and N2-Ar surfaces. The predictive ability of all surfaces with respect to the temperature dependence of the interaction second virial coefficient, BI2(T ), has also been tested. For the N2-Ne system only the present HFD3 surface gives good agreement with the experimental interaction second virial coefficients over a wide temperature range. Similarly, for the Nz-Ar system the surface of Candori et al. [1983, Chem. Phys. Lett., 102, 412], which was partially determined using the second virial coefficient data, and the present HFD1 surface give good agreement with experimental virial data.