Abstract <p>According to Kolmogorov’s hypothesis, in turbulent flows at large Reynolds numbers, there is an extended inertial range of scales in which neither external nor viscous forces play an appreciable role, and all statistical properties are determined by the rate of kinetic energy dissipation. Turbulent flows in which the effect of external forces on scales corresponding to the inertial range is of fundamental importance are common in nature. The usual integrals of motion (e.g., the energy of velocity fluctuations and hydrodynamic helicity) cease to exist, and other quadratic quantities that include scale dependence become integrals of motion. At the same time, cascade processes become non-conservative from the viewpoint of the usual integrals of motion. This idea is developed in the context of shell models of MHD-turbulence and allows special regimes of cascade processes in MHD-turbulence to be described.</p>