A simple technique is suggested for constructing approximate relations with wide ranges of applicability (the same formula can be employed to describe a variety of qualitatively identical problems which differ geometrically, i.e. in the surface shape, flow pattern, etc.). The technique is based on the transition from ordinary dimensionless variables to special asymptotic coordinates. The illustration is made by reference to numerous specific problems in the theories of mass and heat transfer and physicochemical hydrodynamics. Comparison of the relations obtained with a number of typical cases, for which exact, numerical, approximate and asymptotic results are already available, shows a good accuracy and great capabilities of the method. The method can also be used with success in other fields of chemical engineering science, mechanics and physics.