We have studied the dynamics of electrons in single-wall carbon nanotube (bucky paper) samples using femtosecond time-resolved photoemission. The lifetime of electrons excited to the pi* bands is found to decrease continuously from 130 fs at 0.2 eV down to less than 20 fs at energies above 1.5 eV with respect to the Fermi level. This should lead to a significant lifetime-induced broadening of the characteristic van Hove singularities in the nanotube density of states.