The exchange kinetics of macromolecules (e.g. polymers or proteins) desorbing from a solid surface is investigated using a theoretical model which accounts for both transport-controlled and detachment-controlled kinetics in a unified manner. In the transport-controlled regime, the decay has an effectively stretched-exponential behavior with an exponent that could vary anywhere from 0 to 1. The theoretical predictions agree well with the results from dynamic Monte Carlo simulations. The solution presented here will be valuable for interpreting exchange-kinetics experiments and can be used to obtain both the attachment rate and the detachment rate unambiguously.