We investigate the energy band structure, total density of states, the linear, nonlinear optical (NLO) response, and the electron energy-loss spectrum for Li(Nb, Ta)O-3 using first principles calculations based on density functional theory in its local density approximation. Our calculation shows that these compounds have similar structures. The indirect band gaps of 3.39 eV(LiNbO3) and 3.84 eV (LiTaO3) at the Gamma Z direction in the Brillouin zone are found. A simple scissor approximation is applied to adjust the band energy gap from the calculations to match the experimental values. The optical spectra are analyzed and the origins of some of the peaks in the spectra are discussed in terms of calculated electronic structure. Calculations are reported for the frequency-dependent complex second-order NLO susceptibilities chi((2))(ijk)(-2 omega, omega, omega) up to 10 eV and for zero-frequency limit chi((2))(ijk)(0). The results are compared with the theoretical calculations and the available experimental data.