The subject of this study is the comparative analysis of the kinetic mechanisms that proceed in a methane-air mixture when O-2 molecules are excited to the b(1)Sigma(+)(g) electronic state by laser photons with wavelength lambda(I) = 762.346 nm and when O-2 molecules dissociate due to the absorption of laser radiation with lambda(I) = 193.3 nm. The efficiencies of both methods of combustion initiation are compared with each other and against the method of laser-induced thermal ignition. Numerical simulation shows that for methane-air mixture the excitation of O-2 molecules to the b(1)Sigma(+)(g) state is more effective in reducing the induction time and in lowering the ignition temperature than the method of photodissociation of O-2 molecules by laser radiation at 193.3 nm wavelength. In order to ignite a stoichiometric CH4-air mixture at identical temperature it is needed to supply twofold greater energy upon photodissociation of O-2 molecules than in the case of O-2 molecule excitation. However, both the laser-induced excitation of O-2 molecules to the b(1)Sigma(+)(g) state and O-2 molecule dissociation by laser photons with lambda(I) = 193.3 nm are much more effective in combustion initiation than the method based on heating the mixture by laser radiation.