Existing measurements of the collision-induced rototranslational absorption spectra of gaseous mixtures of methane with helium, hydrogen, or nitrogen are compared to theoretical calculations, based on refined multipole-induced and dispersion force-induced dipole moments of the interacting molecular pairs CH4–He, CH4–H2, and CH4–N2. In each case the measured absorption exceeds the calculations substantially at most frequencies. We present the excess absorption spectra, that is the difference of the measured and the calculated profiles, of these supramolecular CH4–X systems at various gas temperatures. The excess absorption spectra of CH4–X pairs differ significantly for each choice of the collision partner X, but show common features (spectral intensities and shape) at frequencies from roughly 200 to 500 cm−1. These excess spectra seem to defy modeling in terms of ad hoc exchange force–induced dipole components attempted earlier. We suggest that besides the dipole components induced by polarization in the electric molecular multipole fields and their gradients, and by exchange and dispersion forces, other dipole induction mechanisms exist in CH4–X complexes that presumably are related to collisional distortion of the CH4 molecular frame.