Turbulent combustion in cylinders can be considered to involve chemistry of two different types, namely fast and slow in comparison with the turbulence. Different methods are needed for addressing these two types of chemistry. Turbulent mixing controls the fast chemistry, which proceeds as rapidly as advancing turbulent fronts allow. Slow chemistry is more oblivious to turbulence and proceeds at rates dependent on local temperature, pressure and chemical composition. Reaction-sheet descriptions thus may be applied to fast chemistry and distributed-reaction descriptions to slow. This work addresses methods for describing combustion processes that treat fast and slow chemistry differently.In premixed charges, the principal heat-release rates are fast. Turbulence modeling is suggested to be sufficient for describing the propagation of the main heat-release fronts. Slow chemistry includes autoignition, CO burnup and NOx production. Most of the elementary chemical rates for these processes are now sufficiently well established that they can be employed in place of empiricism for calculating knock and emissions. Systematically reduced chemistry is employed here to provide rate expressions for relevant slow chemistry.The limit of slow CO oxidation is selected for describing the chemistry involved in CO burnup. Inclusion of thermal and nitrous-oxide mechanisms of NOx production, along with this, yields a simplified description of these post-flame pollutant processes. Calculations with a modified KIVA code, employing k-ε modeling for the fast chemistry and reduced slow chemistry based on slow CO oxidation, produce agreement with measured NOx emissions in a dual-fuel diesel running on natural gas. Reduced chemistry for methane autoignition also produces agreement with observed knock. These concepts of partitioning chemistry into fast and slow groups and treating the two differently thus appear to be potentially helpful for enhancing understanding of knock and emissions and for enabling reasonable, simplified, fundamentally based computational estimates of knock occurrence and emission indices to be made.