The principles of formation of closed and quasiperiodic orbitally stable trajectories of conservative systems are formulated. It is revealed that irregular oscillations are due to the orbital instability of quasiperiodic oscillations. A bistable oscillator with periodic forcing is considered. The existence of random oscillations at low level of energy and the conditions for orbitally stable oscillations are established Keywords: domain of periodic solutions, random oscillations, chaos Introduction. Modern methods of qualitative analysis of motion are based on studies due to Poincaré [11], Birkhoff [3], Lyapunov [7], Andronov [1], etc. (see [4,5,14] and the references therein). In the last 20 years, there have been extensive studies in this area [6,8,13] promoted by applications in mechanics [2,12,15,17,[19][20][21][22][23] and other natural sciences. The concept of complex motions includes chaos, meaning, for example, walk on sections of an orbitally unstable trajectory for an infinite time. An example of regular motion is quasiperiodic motion. The objective of the analysis of conservative systems with complex trajectories is to estimate the domain in which and the energy at which the motions are regular. This can be done with simple (two-frequency) models of mechanical systems with several singular points. Considering classical problems, we attempt to resolve this issue based on the symmetry principle due to 31]. After a preliminary analysis, we will estimate these domain and energy. An analysis of quasiperiodic trajectories shows that they are subject to neutral attraction. By neutral attraction is meant that the integral sum of quasicharacteristic exponents of the system of variational equations is equal to zero. In the periodic case, the domain of existence of a closed trajectory may not be a domain of stable oscillations. By stability of oscillations is meant orbital stability. We will consider a system that has a family of solutions in some domain.1. Preliminaries. Consider a material system with a finite number of degrees of freedom. Its motion is described by the equation