The molecular characteristics of cylindrical first–third generation dendrimers carrying dendrons based on L-aspartic acid are compared. It is shown that both the generation number of side dendrons and their structure determine the conformational, hydrodynamic, optical, and dipole characteristics of dendrite macromolecules. It is found that the studied class of cylindrical dendrimers is distinguished by a marked amount of intramolecular hydrogen bonds between side dendrite substituents. These bonds ensure the unusual combination of high kinetic rigidity and a compact conformation (low equilibrium rigidity) of macromolecules. The rupture of hydrogen bonds leads to an enlargement of molecular coils (an increase in equilibrium rigidity) that is accompanied by a sharp drop in kinetic rigidity.