In the book the resonant problems in different areas of physics, chemistry and biology from a
uniform point of view - extremeness of resonant states of a motion in a nature are considered. The problems of dynamics of a motion and retention of atomic, macroscopic particles, microorganisms in inhomogeneous fields, beyond and inside of resonance conditions; problems of dynamic stability of unstable states, bifurcation, chaos, discreteness, evolution of nonlinear dynamic systems which are not containing in an explicit view a small parameter are analyzed. Fundamentals of the resonant theory of dynamic systems are state. The unsolved problems are marked and the trajectories of their solution, in particular: ball – lightning, activated water, resonant action of superweak fields at biological systems, including correlation between periods of solar Activity and processes happening at this time on the Earth are outlined.