The mathematical theory of minor-constituent neutral-particle diffusion is reviewed and extended to take account of diffusion in an atmosphere with linearly varying scale height. In addition, solutions of sinks and sources (simultaneous production). Various simplified criteria of diffusion which have been used formerly are reviewed, and a general criterion is proposed. Application of the general theory to three particular problems is briefly indicated. In the first, it is shown that under the simultaneous action of diffusion and mixing the molecular oxygen distribution above 100-km altitude must depart from a photochemical equilibrium distribution. Secondly, the downward migration of calcium continuously introduced into the atmosphere by meteor is described ; and, finally, the usefulness is the theory is shown in analyzing the downward migration of nitrogen atoms from a high-level production regions.