We calculated the cross sections for vibrational predissociation of methane-Ar induced by excitation of the methane nu 3 mode with the aid of an ab initio CH4-Ar potential depending explicitly on the nu 3 and nu 1 normal coordinates of the CH4 monomer. We found that dissociation into CH4 fragments excited in the nu 1 mode, a V-->V' process with very low kinetic energy release, strongly dominates over direct dissociation into Ar and ground state CH4, and is responsible for the line broadening observed experimentally. The (observed and calculated) strong variation of the line widths for the Van der Waals levels excited in combination with the nu 3 mode (giving states of A, F and E symmetry) is related to the opening up of appropriate nu 1 dissociation channels and the occurrence of rotational resonances in the nu 1 continuum in the energy range of the quasi-bound nu 3 levels.