We investigate the band-gap modification by radial deformation in BN and BC3 nanotubes through first-principles pseudopotential density-functional calculations. In zigzag BN nanotubes, radial deformations that give rise to transverse pressures of about 10 GPa decrease the gap from 5 to 2 eV, allowing for optical applications in the visible range. When armchair BC3 nanotubes with the gap of about 0.5 eV are collapsed down to the interlayer distance of 3.5 Angstrom, a gap closure occurs due to the lowering of, the unoccupied pi band. On the other hand, the band gaps of armchair BN and zigzag BC3 nanotubes are found to be insensitive to radial deformations. This different behavior between zigzag and armchair nanotubes is attributed to the different characteristics of states near the gap.