We present density functional response theory generalized to triplet excitations. A method based on an exponential parametrization of the spin-dependent density operator is derived for the evaluation of linear and quadratic response functions for spin-dependent perturbations. The developed methodology is applicable to commonly available functionals, also hybrid functionals including exchange-correlation functionals at the general gradient-approximation level and fractional exact Hartree-Fock exchange. Illustrative calculations are presented for singlet-triplet transition moments and phosphorescence lifetimes, providing numerical data on these quantities for the first time using time-dependent density functional theory. (C) 2003 American Institute of Physics.