An implementation of time-dependent density functional theory in various variants is reported. Use is made of the resolution of the identity (RI) approximation for both 'pure' and hybrid density functionals. The transformation of the three-index repulsion integrals to the MO basis leads to significant computational savings (factor 2-4) in the case of hybrid functionals but is not competitive with AO direct algorithms in the case of pure functionals. The error introduced by the RI approximation on the computed transition energies is negligible (<15 cm(-1)). Systematic benchmark calculations are reported. (C) 2002 Elsevier Science B.V. All rights reserved.