Cu(I)-catalyzed azide-alkyne [3 + 2] cycloaddition is used to construct step-by-step covalent polymer or polyelectrolyte multilayers. The catalysis involves the formation of a transient, yet rather stable, positively charged Cu(I)/alkyne complex. We demonstrate that the formation of this complex has a strong influence on the multilayer buildup process. It favors, for example, the film buildup between neutral polymer bearing alkyne groups and polyanion bearing azide groups. In contrary, it disfavors the buildup of the same neutral polymer with polycations bearing azide groups. The constructions of other multilayer systems are investigated and discussed in the light of the electrostatic interactions between these positively charged Cu(I)/alkyne complexes and the polyelectrolytes.