We consider the competitive adsorption of a bidisperse polymer solution of long and short chains onto a flat surface. Starting from an adsorbed layer, mainly formed by short chains, the replacement of short by long chains is studied for fixed and very dilute bulk concentration. Our theory is restricted to the case of weak, reversible adsorption, where the net monomer-surface contact energy is much smaller than the thermal energy. We obtain the following description of the replacement process. After a fast first step which depends on the initial composition of the layer, the structure of the layer changes in a universal way: First, long and short chains are exchanged at almost constant layer thickness until most of the short chains have been replaced. Then, the layer's thickness rapidly grows and saturates at the final equilibrium value. In equilibrium the layer predominantly consists of long chains.