ultiwalled carbon nanotubes, prepared by both electric arc discharge and chemical vapor deposition methods, show a strong visible light emission in photoluminescence experiments. All the samples employed in the experiments exhibit nearly same super-linear intensity dependence of the emission bands on the excitation intensity, and negligible temperature dependence of the central position and the line shapes of the emission bands. Based upon theoretical analysis of the electronic band structures and optical transition, it is suggested that besides the electronic transitions across the fundamental gap, the transitions between pi and sigma conduction bands are the major source of the light emissions. A two-step transition mechanism is proposed.