A new family of selective four-wave mixing methods, based on the estab
lishment of vibrational nonlinear polarizations with multiple resonanc
es, is proposed. This family includes double-infrared resonances, vibr
ationally enhanced Raman resonance, and vibrationally enhanced two-pho
ton resonance. These methods are related to traditional Raman and infr
ared spectroscopy, but the methods are shown to have the capabilities
for component and conformer selectivity, line-narrowing of inhomogeneo
usly broadened vibrational transitions, and mode selection. The theore
tical foundations for the methods are developed and directed to possib
le applications.