A series of time-resolved IR-IR double-resonance experiments have been conducted where methane molecules are excited into a selected rovibrational level of the 2nu3(F2) vibrational substate of the tetradecad and where the time evolution of the population of the various energy levels is probed by a tunable continuous wave laser. The rotational relaxation and vibrational energy transfer processes occurring in methane upon inelastic CH4-H2 and CH4-He collisions have been investigated by this technique at room temperature and at 193 K. By probing transitions in which either the lower or the upper level is the laser-excited level, rotational depopulation rates in the 2nu3(F2) substate were measured. The rate constants for CH4-H2 collisions were found to be 17.7 +/- 2.0 and 18.9 +/- 2.0 micros(-1) Torr(-1) at 296 and 193 K, respectively, and for CH(4)-He collisions they are 12.1 +/- 1.5 and 16.0 +/- 2.0 micros(-1) Torr(-1) at the same temperatures. The vibrational relaxation was investigated by probing other stretching transitions such as 2nu3(F2) - nu3, nu3 + 2nu4 - 2nu4, and nu3 + nu4 - nu4. A kinetic model, taking into account the main collisional processes connecting energy levels up to 6000 cm(-1), that has been developed to describe the various relaxation pathways allowed us to calculate the temporal evolution of populations in these levels and to simulate double-resonance signals. The different rate coefficients of the vibrational relaxation processes involved in these mixtures were determined by fitting simulated signals to the observed signals corresponding to assigned transitions. For vibration to translation energy transfer processes, hydrogen is a much more efficient collision partner than helium, nitrogen, or methane itself at 193 K as well as at room temperature.