This Thesis is devoted to theoretical investigation of the effective magnetic properties of nonlinear metamaterials, based on resonant conductive elements.A general expression for the effective bulk ermeability in the microwave frequency range is derived. Frequency dispersion of the permeability is studied and recommendations for optimisation of metamaterials with negative permeability are given. The results are supported with numerical simulation of the finite metamaterial sample.Next, a metamaterial possessing nonlinear magnetic responseowing to nonlinear electronic components, inserted into resonant conductive elements, is proposed. For the limit of low nonlinearity, the arising quadratic nonlinear susceptibility is calculated; it is shown how it is controlled by the properties and arrangement of the structure elements as well as by the type and characteristics of the insertion.For the insertions operating in essentially nonlinear regime, when a nonlinear magnetic susceptibility cannot be introduced, an approach is developed for analyzing three-wave coupling processes with a strong pump wave and two weak signals. Peculiarities of coupling, arising from use the insertions with variable resistance or variable capacitance are discussed. Estimates are given that extremely strong nonlinear coupling can be achieved using typical diodes reported in literature.Finally, it is demonstrated how the metamaterial band gap can be tuned, and the resulting metamaterial switching between transmitting, reflecting and absorbing states is described. The details appear to depend drastically on the type of nonlinear components inserted into the resonant conductive elements. Relying on practical estimates, it is predicted that the transmittance of a metamaterial slab can be modulated by several orders of magnitude already using a slab with thickness equal to one microwave wavelength in vacuum.