In the review the results on the modeling of angular oscillations of the nitrous bases in short and long (in the limit - infinite) fragments of polynucleotide DNA chains are collected and systematized. The material is arranged so to represent the results of investigations in the course of development beginning from those obtained first for elementary models as the pendulum or a pair of coupled unequal pendulums, and then for more complex DNA models. The description of dynamic behavior features of all considered model systems is executed in the uniform mathematical language representing a state of model system as a point, moving along a certain trajectory in the phase space.