1. There is a non-linear decrease in the protein fluorescence (F) of lactate dehydrogenase with the increase in the fraction (alpha) of the coenzyme-binding sites occupied with NADH. 2. By a curve-fitting procedure it is shown that the fluorescence intensity can be represented by the equation F=[1-alpha(1-x)](n) where n is the number of identical and indistinguishable coenzyme-binding sites per protein molecule and x=F(s) (1/n) (F(s) is the protein fluorescence at alpha=1). This equation implies that the relative protein fluorescence of molecules bearing j ligands form the geometric series x(j). 3. Non-linear quenching of protein fluorescence for this enzyme is probably due to radiationless transfer of energy from the protein molecule to the bound NADH and should also be observed when other potential acceptors of protein fluorescence are bound at unique sites. 4. The intercept with F(s) of an initial tangent to a curve of protein fluorescence against alpha will be at a value of alpha equal to (K(d)+[E(0)]). (1-x(n))/n.(1-x) and not at a value equal to the sum of the dissociation constant (K(d)) and the concentration of identical ligand-binding sites ([E(0)]). 5. A use of non-linear protein fluorescence quenching to investigate the state of aggregation of a protein is discussed.