  The generating function for elements of the Bethe subalgebra of Hecke algebra
is constructed as Sklyanin's transfer-matrix operator for Hecke chain. We show
that in a special classical limit q -> 1 the Hamiltonians of the Gaudin model
can be derived from the transfer-matrix operator of Hecke chain. We consruct a
non-local analogue of the Gaudin Hamiltonians for the case of Hecke algebras.
