  We propose a method of constructing completely integrable systems based on
reduction of bihamiltonian structures. More precisely, we give an easily
checkable necessary and sufficient conditions for the micro-kroneckerity of the
reduction (performed with respect to a special type action of a Lie group) of
micro-Jordan bihamiltonian structures whose Nijenhuis tensor has constant
eigenvalues. The method is applied to the diagonal action of a Lie group $G$ on
a direct product of $N$ coadjoint orbits $\O=O_1\times...\times O_N$ endowed
with a bihamiltonian structure whose first generator is the standard symplectic
form on $\O$. As a result we get the so called classical Gaudin system on $\O$.
The method works for a wide class of Lie algebras including the semisimple ones
and for a large class of orbits including the generic ones and the semisimple
ones.
