  We present an ``algebraic treatment'' of the analytical Bethe ansatz for open
spin chains with soliton non preserving (SNP) boundary conditions. For this
purpose, we introduce abstract monodromy and transfer matrices which provide an
algebraic framework for the analytical Bethe ansatz. It allows us to deal with
a generic gl(N) open SNP spin chain possessing on each site an arbitrary
representation. As a result, we obtain the Bethe equations in their full
generality. The classification of finite dimensional irreducible
representations for the twisted Yangians are directly linked to the calculation
of the transfer matrix eigenvalues.
