Time-dependent density functional theory (TD-DFT) is applied to model one-photon (OPA) and two-photon (TPA) absorption spectra in a series of conjugated cytotoxic dyes. Good agreement with available experimental data is found for calculated excitation energies and cross sections. Calculations show that both OPA and TPA spectra in the molecules studied are typically dominated by two strong peaks corresponding to different electronic states. We find that donor-acceptor strengths and conjugated bridge length have a strong impact on the cross-section magnitudes of low- and high-frequency TPA maxima, respectively. These trends are analyzed in terms of the natural transition orbitals of the corresponding electronic states. Observed structure-property relationships may have useful implications on design of organic conjugated chromophores with tunable two-photon absorption properties for photodynamic therapy applications.