  We present a general derivation of semi-fermionic representation for
generators of SU(N) group as a bilinear combination of Fermi operators. The
constraints are fulfilled by means of imaginary Lagrange multipliers. The
important case of SU(2) group is discussed. We demonstrate how the idea of
semi-fermionic representation might be extended to the groups possessing
dynamic symmetries. As an example, SO(4) group is considered. We illustrate the
application of semi-fermionic representations for various problems of strongly
correlated physics.
