The second-order nonlinear optical susceptibility (χ (2) abc ) and linear electro-optical coefficient (r abc ) of a large number of single-walled zigzag, armchair and chiral SiC nanotubes (SiC-NTs) as well as bulk SiC polytypes (2H-, 4H-, 6H-and 3C-SiC) and single graphitic SiC sheet have been calculated from first-principles. The calculations are based on density functional theory in the local density approximation and highly accurate full-potential projector augmented-wave method is used. Both the zigzag and chiral SiC-NTs are found to exhibit large second-order nonlinear optical behavior with the χ (2) abc and r abc coefficients being up to ten-times larger than that of bulk SiC polytypes, and also being up to thirteen-times larger than the counterparts of the corresponding BN-NTs, indicating that SiC-NTs are promising materials for nonlinear optical and opto-electric applications. The prominant features in the spectra of χ