  We present an algebraic study of a kind of quantum systems belonging to a
family of superintegrable Hamiltonian systems in terms of shape-invariant
intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or
$(su(p,q),so(2p,2q))$. The eigenstates of the associated Hamiltonian
hierarchies belong to unitary representations of these algebras. It is shown
that these intertwining operators, related with separable coordinates for the
system, are very useful to determine eigenvalues and eigenfunctions of the
Hamiltonians in the hierarchy. An study of the corresponding superintegrable
classical systems is also included for the sake of completness.
