Resonantly enhanced infrared laser-induced desorption of methane condensed on a single-crystal NaCl(100) surface is observed after excitation with the widely tunable infrared laser output of the free-electron laser at the free-electron laser for infrared experiments facility using mass spectroscopic detection and time-of-flight analysis. Desorption of methane is observed only when the exciting light is in resonance with an internal vibrational mode of the molecule. Different intramolecular modes of the three methane isotopologues under study--CH(4), CD(4), and CD(3)H--are excited; the degenerate deformation mode nu(4) is observed for CH(4) and CD(4) at 7.69 and 10.11 microm, respectively, as well as the nu(2) and nu(4) modes of CD(3)H at 7.79, 9.75, and 9.98 microm. The desorption signals for the pure layers of these different methane isotopologues as well as for different mixtures of two of these are investigated as a function of the infrared wavelength and the laser fluence. The desorption behavior for pure and mixed layers is compared and the underlying desorption mechanism is discussed.