The laminar flamelet structures of methane/air, propane/air, and hydrogen/air nonpremixed combustion at low and vanishing scalar dissipation rates are investigated, by numerical calculations of a system of conservation equations in a counterflow diffusion flame configuration, together with a transport equation defining the mixture fraction and scalar dissipation rate. The chemical reaction mechanisms consist of 82 elementary reactions up to C-3 species. In the limit of vanishing scalar dissipation rate, two types of structures are shown to appear. In one structure fuel and oxygen are consumed in a thin layer located near the stoichiometric mixture fraction, Z(st), where the temperature and the major products reach their peaks. This is similar to the so-called Burke-Schumann single layer flame sheet structure. One example is the hydrogen/air diffusion flame. The second structure consists of multilayers. Fuel and oxygen are consumed at different locations. Oxygen is consumed at Z(l) (near Z(st)), where the temperature and the major products reach their peaks. Fuel is consumed at Z(r) (> Z(st)). Between Z(l) and Z(r) some intermediate and radical species are found in high concentrations. Hydrocarbon/air nonpremixed flames are of this type. It is shown that for methane/air diffusion flames, some chemical reactions which are negligible at large scalar dissipation rate near flame quenching conditions, play essential roles for the existence of the multilayer structure. Examples of such reactions are, CH4 --> CH3 + H, H2O + O-2 --> HO2 + OH, H2O + M --> H + OH + M and CHO + H-2 --> O + H. The sensitivity of the species distributions in the flamelet to the scalar dissipation rate varies for different species. The most sensitive species are the intermediates and radicals at the fuel-rich side. At low scalar dissipation rate the radiative heat transfer can significantly move the fuel consumption layer to the oxygen consumption layer, increase the oxygen leakage to fuel side, and even quench the flame. Differential diffusion modifies the species and temperature profiles in the flamelet, but does not affect the multilayer nature of the flamelet. This result is used to successfully explain the high CO emissions in a turbulent methane/air diffusion flame.