The rotational dynamics, i.e., tunneling and almost free quantum rotation at low temperature and rotational diffusion at higher temperature, have been studied in methane–argon mixtures in the whole concentration range and at temperatures up to T=40 K. Changes of the rotational spectra allow parts of the phase diagram to be established in detail. At T=5 K, a transition from a perturbed partially ordered phase II to be a disordered glassy phase has been observed at an argon concentration of 10%. There is a small regime of coexistence of these two phases. The miscibility gap at larger argon concentrations is wider than determined by x-ray diffraction with methane being almost insoluble in argon.