The resistance of single-walled carbon nanotube (SWNT) bundles has been investigated by two-terminal measurements. We find that the time dependence of resistance (dR/dt) exhibits different behaviors at different currents. At low currents, a positive dR/dt is observed. However, dR/dt shows a negative sign when the applied current exceeds a critical current (Ic). Ic coincides with the current when the sample begins to emit light. The variation of dR/dt can be interpreted as the thermal effects owing to Joule heating in the SWNTs. Our lighting SWNTs sample has a small change in resistance and exhibits high stability.