Background and Objectives: The nonlinear phase of the development of Parker’s instability of large-scale oscillations of magnetic fields at various depths of the convective zone of the Sun up to the stage of saturation is investigated. Materials and Methods: Based on the conservative difference scheme, an algorithm for calculating the dynamics of a thin magnetic tube when moving in the convective zone and the solar atmosphere is presented. The equilibrium conditions of the position of the magnetic tube at various depths of the convective zone are determined. The types of linear oscillations of the tube near the equilibrium position are defined: fast (Alfven) and slow (varicose) waves. Results: The calculation has revealed the realization of quasilinear oscillations of emerging magnetic fields near the photospheric level, generating a steady stream of weak shock waves in the lower layers of the solar atmosphere. It has been shown that the development of Parker’s instability in the low-frequency part of the spectrum of global oscillations of magnetic fields provides a stable, spherically symmetric structure of anomalous heating in the era of the minimum solar activity cycle. With an increase in the frequency of global oscillations of magnetic fields at the stage of growth of the cycle activity, the structure of anomalous heating becomes spatially inhomogeneous – radiation. Conclusion: The number of rays of anomalous heating with the development of the activity cycle monotonously increases and, in the era of maximum activity, passes into a spatially uniform structure of anomalous heating of the atmosphere in accordance with the observed data.