Two possible reaction paths for the CH3 + C2H5 System are direct hydrogen abstraction or association reaction. In the present study, the kinetics of the two possible reactions are investigated from a theoretical point of view. Unimolecular dissociation of propane is also studied. As one expects, association or dissociation reactions are pressure dependent processes, while hydrogen abstraction reaction is not sensitive to the pressure. Potential energy surfaces for both reaction paths are explored by UMP2, CAS, QCISD, and DF-F methods. Energies of stationary points were calculated by CASMP2, B3LYP, MP4SDTQ, and QCISD methods. Canonical variational transition-state theory and microcanonical variational RRKM calculations were used to locate the position of bottleneck for the association reaction of methyl and ethyl radicals. The RRKM method was used to calculate the pressure dependency of the rate constants for dissociation of propane and association of methyl and ethyl radicals. Conventional transition-state theory was used to calculate the rate constant for hydrogen abstraction reaction of the two radicals in the title in a temperature range of 200-2500 K. According to our RRKM calculations, the high-pressure Arrhenius parameters for dissociation reaction of propane and association reaction of the two radicals were found as k(-1) = 1.1 x 10(17) exp(-369.1 kJ mol(-1)/RT) s(-1) and k(1) = 5.5 x 10(11) T-0.56 exp(0.53 kJ mol(-1)/RT) L mol(-1)s(-1). According to generalized transition-state theory, the rate constant for hydrogen abstraction reaction were found as k(2) = 9.8 x 10(8) L mol(-1)s(-1) over the temperature range of 200-2500 K.