We calculate the linear and nonlinear optical response of GaN and AlN in the wurtzite structure. The dielectric function ⑀(), the second harmonic generation susceptibility (2) (Ϫ2;,), and the linear electro-optic susceptibility (2) (Ϫ;,0) are all evaluated over a broad frequency range. These results are based on a first principles electronic structure calculation using the full-potential linearized augmented planewave method within the local density approximation. Corrections to the underestimation of the band gaps are included at the level of the scissors approximation, which is carefully incorporated within our susceptibility formalism. All independent components for the response functions are calculated; the results for GaN and AlN are very different, and those of AlN are in strong disagreement with predictions of the bond charge model. Results for all response functions at zero frequency are underestimated with respect to the available experimental values. A comparison of the calculated response functions for nonzero frequencies is made with the limited experimental data. We confirm both analytically and numerically that the calculated second-order susceptibilities obey various symmetry constraints below the band gap. ͓S0163-1829͑97͒04019-8͔

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