Exhaust dyeing reactive dyes on cellulose involves inorganic and dye ions in two phases, liquid and solid, dyebath and fiber. Chemical reactions can take place in the bath or in the fiber, but the physical processes often involve those ions which can move reversibly from dyebath to fiber and back again. Other ions and molecules, particularly cellulose and cellulose deriva- tives, are not mobile. The situation can be represented in a simple diagram, Table I, which indicates solution and fiber phases, those mobile ions which attempt to equili- brate between dyebath and fiber (double arrows) and the immobile species. It is no easy matter to scientifically study all these ion movements and equilib- ria while studying chemical reaction rates as well. The next sections outline a method which is very helpful in such an attempt. The same general approach has proved useful for studying the acid dyeing of nylon and the basic dyeing of acrylics (7). However, the next three short sections may be of little interest to dyers.