In this paper we apply the master equation approach to study the effects of the energy landscape topology and topography on the kinetics of folding, and on kinetic transitions of three alanine-hexapeptides analogs which involve polypeptides with neutral and charged groups and a cyclized polypeptide. We rely on the potential-energy landscapes of these molecular systems, which have been constructed using both a topological mapping analysis and a principal component analysis. It was found that the different topology and topography of the energy landscapes result in different "folding" time scales and that the systems with geometrical constraints (cyclization and opposite charges at the termini) "fold" more slowly than the unconstrained peptide. In addition, for each of the three polypeptide systems, the kinetics is nonexponential at the temperature range 400-600 K. The relaxation kinetics is characterized by logarithmic oscillations, which indicate hierarchical dynamics characterized by multiple time scales of fast (few ps) and slow (few mus) events. At higher temperatures, successive relaxation channels with similar characteristic time scales collapse into a single relaxation channel. While the kinetics of the unconstrained peptide at 600 K can be reasonably well described by a single exponential time scale, the kinetics of the constrained hexapeptides are inherently hierarchical and featured by multiple time scales even at high temperatures.