Restricted and unrestricted forms of time-dependent Hartree-Fock theory have been implemented and used to study the electronic dynamics of ethene, benzene, and the formaldehyde cation subjected to both weak and strong oscillating electric fields. Absorption spectra and frequency-dependent polarizabilities are calculated via the instantaneous dipole moment and its derivative. In the weak field limit the computed excitation energies agree very well with those obtained using linearized time-dependent Hartree-Fock theory, which is valid only in the low-field perturbation limit. For strong fields the spectra show higher-order excitations, and a shift in the position of the excitations, which is due to the nonadiabatic response of the molecules to the field. For open-shell systems in the presence of strong oscillating electric fields, unrestricted time-dependent Hartree-Fock theory predicts the value of S2 to vary strongly with time.