The linear and nonlinear polarizabili ties of hydrogen-terminated Ga-m NnHx (m = n = 1, 4, 7, 17) clusters have been calculated by the ab initio time-dependent Hartree-Fock method. The calculated linear polarizability per Ga-N unit for the Ga17N17H38 cluster shows excellent agreement with the corresponding value estimated from the measured dielectric constant of bulk GaN. The calculated (hyper)polarizabilities show a strong dependence upon the size and the geometry of the cluster. For clusters containing equal numbers of Ga and N atoms but differing in geometry, the structure with a reduced symmetry has a much larger first-order NLO coefficient than that with a higher symmetry. Published by Elsevier B.V..