We consider six different secondary structures of proteins and construct two types of Go-type off-lattice models: with the steric constraints and without. The basic amino acid-amino acid potential is Lennard-Jones for the native contacts and a soft repulsion for the non-native contacts. The interactions are chosen to make the target secondary structure be the native state of the system. We provide a thorough equilibrium and kinetic characterization of the sequences through the molecular dynamics simulations with the Langevin noise. Models with the steric constraints are found to be better folders and to be more stable, especially in the case of the beta structures. Phononic spectra for vibrations around the native states have low frequency gaps that correlate with the thermodynamic stability. Folding of the secondary structures proceeds through a well-defined sequence of events. For instance, alpha helices fold from the ends first. The closer to the native state, the faster establishment of the contacts. Increasing the system size deteriorates the folding characteristics. We study the folding times as a function of viscous friction and find a regime of moderate friction with the linear dependence. We also consider folding when one end of a structure is pinned which imitates instantaneous conditions when a protein is being synthesized. We find that, under such circumstances, folding of helices is faster and that of the beta sequences slower. (C) 2000 American Institute of Physics. [S0021-9606(00)51615-8].