We have recorded, in absorption, infrared spectra of samples of methane, CH 4 and CD 4 , dispersed at molar fraction 0.0001–0.005 in solid neon, in solid argon and in their equimolar solid mixture in the temperature range 3–21K and in the spectral domain 5000–500cm −1 at resolution 0.04–0.2cm −1 . We undertook quantitative fitting of the spectral profiles with components of gaussian and lorentzian shapes. Comparison of our spectra in regions of fundamental modes both ν 3 and ν 4 with published spectra of CH 4 and CD 4 in either crystalline para-dihydrogen or droplets of liquid helium indicates evidence for hindered rotation of CH 4 molecules in Ar but not for rotation of CH 4 or CD 4 in Ne or in a mixture of Ne and Ar. For CD 4 in solid Ar, the evidence for even hindered rotation is ambiguous. We make new assignments of lines to 13 CH 4 and 13 CD 4 in their environments in solid Ne and Ar.