  In this thesis we have obtained and studied the complete set of superfield
equations of motion for the interacting system of four-dimensional
supermembrane and dynamical scalar multiplet. This study provides the first
example of superfield equations for interacting system involving matter
superfields and extended supersymmetric object, as well as the first set of
superfield equations of motion for a dynamical system which includes
supermembrane. The action for a supermembrane in a N = 1 D = 4 chiral
superfield background has been also presented for the first time. We have
obtained the complete set of equations of motion in spacetime components for
the interacting system of dynamical D = 4 N = 1 supergravity and supermembrane
from the superfield equations. To this end we have developed the Wess - Zumino
approach type to Grisaru - Siegel - Gates - Ovrut - Waldram special minimal
supergravity characterized by a dynamically generated cosmological constant. We
have also found the superfield equations in N-extended tensorial superspaces
with N = 2,4 and 8, which describe the D = 4 supermultiplets of massless
conformal higher spin theory with N-extended supersymmetry. On the other hand,
we have obtained the equations of motion of the system of multiple M0-brane
derived from the covariant, supersymmetric and kappa-symmetric action proposed
for such a system . We have also studied the gauge symmetries of the action
which allows us to find the final form of the bosonic equations of motion for
the center of energy coordinate functions. We have also shown that all BPS
states of the system are (1/2)BPS states and have the same properties as the
BPS states of a single M0-brane.
