Using coherent anti-Stokes Raman spectroscopy (CARS) the spectral shift and width of the collisionally narrowed Q-branch structures of nitrogen and the nu(1) symmetric stretch vibration in methane were investigated at high densities. The gas samples either contained the pure substance or, for the case of nitrogen and methane, were diluted with argon, methane and carbon monoxide or argon and nitrogen, respectively, in the pressure range 50-2000 bar and at temperatures between 300 and 700 K. The simultaneous recording of spectra at ambient conditions ensured a frequency measurement accuracy of 0.07 cm(-1). Contributions to the line shapes and frequency shifts are determined that originate from narrowing of the rotational structure and from vibrational dephasing in nitrogen, methane, and its mixtures. The results are compared with quasiclassical calculations of the band shape and shift to determine thermally averaged collision cross sections for energy relaxation and vibrational dephasing as a function of temperature. In the investigated density regime, for nitrogen the band shape is dominated by collisional narrowing. The peak position of the band does not strongly depend on composition of the sample and the maximum red shift of the Raman frequency diminishes with increasing temperature. For methane at densities above 50 amagat effects from rotational relaxation are no longer detectable and dephasing collisions are dominant. In addition to vibration-translation relaxation, vibrational energy transfer is an important process for line broadening at high densities. The frequency shift of the e-band strongly depends on mixture composition and temperature.