The structure of laminar diffusion flames is analyzed in the limiting case of large, although finite, reaction rates. It is shown that the the chemical reaction takes place only in a very thin region or "chemical boundary layer" where convection effects may be neglected. Then the temperature and mass fraction distributions within the reaction zone are obtained analytically. The flame position, rates of fuel consumption, and temperature and concentration distributions outside the reaction zone may be obtained by using the assumption of infinite reaction rates. For large Reynolds numbers mixing and combustion take place in boundary layers and free mixing layers. And again analytical solutions are obtained for the temperature and mass fraction distributions outside of the reaction zone.