  Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which
differ from deformations of Lie algebras in terms of Cartan subalgebra and root
vectors and which make it possible to construct representations by operators
acting according to Gel'fand--Tsetlin-type formulas. Unitary representations of
the q-deformed algebras U_q(so_{n,1}) are found.
