The transport fluxes in multicomponent flame systems due to diffusion and thermal conduction, and to thermal diffusion and its reciprocal effect, are considered from the standpoint of the extension of the Chapman-Enskog kinetic theory to polyatomic gases by Wang Chang, Uhlenbeck & de Boer (1951, 1964) and the subsequent development by Mason, Monchick and coworkers (1961-66). Equations are given for the various diffusional, thermal diffusional and thermal fluxes which it is necessary to derive in order to obtain reaction rates from experimental temperature and composition profiles in flames; and the organization of computer programs for calculation of the multicomponent diffusion and thermal diffusion coefficients and the thermal conductivity is described. The use of matrix partitioning techniques in suitable circumstances to reduce the amount of computation is also discussed. The expressions for the transport fluxes are next used to derive equations for the mole fraction and temperature gradients in flowing reaction systems such as flames where transport processes and reaction occur side by side. From the mole fraction and temperature at one point in the system it is then possible by a numerical integration method such as the Runge-Kutta procedure to compute the complete composition and temperature profiles. Two methods of obtaining the mole fraction and temperature gradients are described, one of which, the Stefan-Maxwell formulation, leads to the more economical computation. A hydrogen-oxygen-nitrogen-steam mixture was chosen under conditions which simulated the pre-reaction region of a hydrogen-oxygen-nitrogen flame that had been studied experimentally, and the detailed composition profiles due to diffusion were computed. The experimental method of measurement involved continuous sampling from the flame and mass spectrometric analysis, a technique which had not previously been checked on a flame system itself. Good agreement between theory and experiment was found when thermal diffusion was considered in the calculation, although the computed hydrogen profile was slightly displaced with respect to the experimental one. This last observation is possibly due to diffusion effects in the pressure gradient at the probe tip. Otherwise the experimental technique seemed to be satisfactory. The computed profiles also showed a number of interesting features such as a maximum in the nitrogen concentration profile caused by thermal diffusion effects.