  We study analogues of the Yangian of the Lie algebra $gl_N$ for the other
classical Lie algebras $so_N$ and $sp_N$. We call them twisted Yangians. They
are coideal subalgebras in the Yangian $Y(gl_N)$ of $gl_N$ and admit
homomorphisms onto the universal enveloping algebras $U(so_N)$ and $U(sp_N)$
respectively. In every twisted Yangian we construct a family of maximal
commutative subalgebras parametrized by the regular semisimple elements of the
corresponding classical Lie algebra. The images in $U(so_N)$ and $U(sp_N)$ of
these subalgebras are also maximal commutative.
