  A method of constructing a class of bihamiltonian structures is presented.
Elements of this class are generalizations of the so-called bihamiltonian
structures of general position on odd-dimensional manifolds. The method
consists in a simultaneous reduction of both the real and imaginary parts of a
complex symplectic form. Necessary and sufficient conditions of getting a
bihamiltonian structure from the mentioned class are obtained. The second part
of the paper is devoted to a series of examples of such a reduction related to
semisimple Lie algebras.
