This thesis is concerned with computational studies of laminar flame structures using detailed and skeletal chemical kinetic mechanisms. Elementary reactions in these mechanisms control the observable combustion properties such as flame speed, autoignition temperature, ignition delay time, and extinction characteristics in nonpremixed and premixed flame phenomena. First part of thesis deals with computational investigations of influence of carbon monoxide and hydrogen addition on methane flames stabilized in counterflow configuration. Computations were performed employing detailed chemical kinetic mechanism — the San Diego mechanism. In case of nonpremixed flames, effect of carbon xvi monoxide addition on structure and critical condition of extinction were examined. Differences between addition on fuel and oxidizer sides were investigated and plausible explanation given for the differences. For premixed flames, effect of addition of hydrogen and carbon monoxide to reactant mixture was studied. Critical conditions of extinction were predicted using computations for various compositions. Rates of production and consumption of various species were calculated and flame structure was analyzed for nonpremixed and premixed flames. It was found that moderate amount of carbon monoxide addition to methane enhances flame reactivity. However, with large amount of carbon monoxide addition, additive chemistry dominates. Addition of increasing amounts of hydrogen in premixed reactant stream enhances methane flame reactivity. In second part of thesis, kinetic modeling was performed to elucidate the structure and mechanism of extinction and autoignition of nonpremixed toluene flames in counterflow configuration. Computations were performed using detailed chemistry to determine flame structure and to obtain values for critical conditions of extinction and autoignition. Sensitivity analysis of rate parameters, reaction pathway analysis, and spatial reaction rate profiles were used to identify reactions controlling critical conditions of autoignition and extinction. Reactions were classified based on reaction rates and sensitivities of species to rate parameters. Chemical kinetic pathways of toluene consumption leading to formation of hydrogen and carbon monoxide were analyzed. All three analyses were employed to form a skeletal mechanism consisting fewer species and reactions than the original detailed mechanism. Predictions from skeletal mechanism of xvii flame structures and critical conditions of extinction and autoignition were found to agree with those from detailed mechanism.