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In this thesis we have obtained and studied the complete set of superfieldequations of motion for the interacting system of four-dimensionalsupermembrane and dynamical scalar multiplet. This study provides the firstexample of superfield equations for interacting system involving mattersuperfields and extended supersymmetric object, as well as the first set ofsuperfield equations of motion for a dynamical system which includessupermembrane. The action for a supermembrane in a N = 1 D = 4 chiralsuperfield background has been also presented for the first time. We haveobtained the complete set of equations of motion in spacetime components forthe interacting system of dynamical D = 4 N = 1 supergravity and supermembranefrom the superfield equations. To this end we have developed the Wess - Zuminoapproach type to Grisaru - Siegel - Gates - Ovrut - Waldram special minimalsupergravity characterized by a dynamically generated cosmological constant. Wehave also found the superfield equations in N-extended tensorial superspaceswith N = 2,4 and 8, which describe the D = 4 supermultiplets of masslessconformal higher spin theory with N-extended supersymmetry. On the other hand,we have obtained the equations of motion of the system of multiple M0-branederived from the covariant, supersymmetric and kappa-symmetric action proposedfor such a system . We have also studied the gauge symmetries of the actionwhich allows us to find the final form of the bosonic equations of motion forthe center of energy coordinate functions. We have also shown that all BPSstates of the system are (1/2)BPS states and have the same properties as theBPS states of a single M0-brane.

On Supermembrane in D=4, multiple M0-brane in D=11 and Supersymmetric Higher Spin Theories