The values of the ignition temperature are experimentally determined and the effective activation energies of the limits of catalytic ignition of mixtures ((40-70%) H-2 + (60-30%) CH4)(stoich) + air over metallic rhodium at a pressure of 1.7 atm in the temperature range of 20 to 300 degrees C are estimated. Above the rhodium surface treated with ignitions, the catalytic ignition temperature of a mixture of 70% H-2 + 30% CH4 + air is 62 degrees C, which indicates the possibility of using rhodium to significantly reduce the ignition temperature of fuels based on hydrogen-methane mixtures. The critical nature of the implementation of the bulk reaction is experimentally discovered: the bulk process occurs at [H-2] = 45%, but is absent at hydrogen concentrations of <= 40%. If [H-2] <= 40%, only a slow surface catalytic reaction occurs. This phenomenon is illustrated by a qualitative calculation. It is established that the effective activation energies of both the upper and lower limits of the catalytic ignition of stoichiometric mixtures of H-2 + CH4 in the linearity range are approximately (2.5 +/- 0.6) kcal/mol. This means that the key reactions responsible for the occurrence of the upper and lower limits of catalytic ignition are the same. It is shown that, in the case of catalysis with a rhodium catalyst, the chain propagation process is most likely of a heterogeneous nature, since the effective activation energy is less than 3 kcal/mol.