  We construct a new family of infinite-dimensional quasi-graded Lie algebras
on hyperelliptic curves. We show that constructed algebras possess infinite
number of invariant functions and admit a decomposition into the direct sum of
two subalgebras. These two facts together enables one to use them to construct
new integrable finite-dimensional hamiltonian systems. In such a way we find
new integrable hamiltonian systems, which are direct higher rank
generalizations of the integrable systems of Steklov-Liapunov, associated with
the e(3) algebra and Steklov-Veselov associated with the so(4) algebra.
