Based on the Ehrenfest theorem, an equation-of-motion that takes relaxation into account has been presented in wave function theory, and the resulting response functions are non-divergent in the off-resonant as well as the resonant regions of the spectrum. The derivation of the linear and first-order nonlinear response functions includes exact state theory as well as single determinant approximate state theory thereby including time-dependent Hartree-Fock and Kohn-Sham theories. The response functions in this theory are complex and the methodology is coined the complex polarization propagator technique. The real and imaginary parts of the response functions may correspond to different physical observables. The present work includes applications that involve electric- and magnetic-dipole molecular properties in the visible, ultra-violet, and X-ray regions of the frequency spectrum. The real and imaginary parts of the electric-dipole polarizability and the mixed electric-dipole-magnetic-dipole polarizability are determined for S-methyl oxirane in order to calculate the polarizability, linear absorption cross section, optical rotatory dispersion, and electronic circular dichroism. The linear absorption cross section is determined in the ultra-violet region and at the carbon K-edge. The polarizability with an imaginary frequency argument is determined for formaldehyde, acetaldehyde, acetone, and methyl oxirane and the related C6, dispersion interaction coefficients are determined from the Casimir-Polder integral. As a single application of the nonlinear response function, the two-photon resonant enhanced second-harmonic generation response is determined for a -two-dimensional- pi-conjugated system.