Solutions are obtained that describe the time dependence of the reversible binding of a ligand to a two‐site lattice. The binding may be cooperative. Three methods are used to obtain these solutions: the separation of on/off processes with a variable transformation, the asymptotic series analysis, and the singular perturbation procedure. Applications to parameter calculation from experimental data are presented. This kinetic system is such that it is difficult to extract all kinetic parameters from data analysis, and the implications for each method are also discussed.