Two-photon-resonant hyper-Raman spectra are reported for three "push-pull" conjugated organic chromophores bearing -NO2 acceptor groups, two dipolar and one octupolar. The excitation source is an unamplified picosecond mode-locked Ti:sapphire laser tunable from 720 to 950 nm. The linear resonance Raman spectra of the same molecules are measured using excitation from the laser second harmonic. Excitation on resonance with the lowest-lying band in the linear absorption spectrum yields nearly identical resonance Raman and resonance hyper-Raman spectra. However, excitation into a region that appears to contain more than one electronic transition gives rise to different intensity patterns in the linear and nonlinear spectra, indicating that different transitions contribute differently to the one-photon and two-photon oscillator strength. The promise of the hyper-Raman technique for examining electronic transitions that are both one- and two-photon allowed is discussed. (C) 2004 American Institute of Physics.