  The $D$-dimensional Smorodinsky-Winternitz system, proposed some years ago by
Evans, is re-examined from an algebraic viewpoint. It is shown to possess a
potential algebra, as well as a dynamical potential one, in addition to its
known symmetry and dynamical algebras. The first two are obtained in
hyperspherical coordinates by introducing $D$ auxiliary continuous variables
and by reducing a 2D-dimensional harmonic oscillator Hamiltonian. The su(2D)
symmetry and ${\rm w}(2D) \oplus_s {\rm sp}(4D,{\mathbb R})$ dynamical algebras
of this Hamiltonian are then transformed into the searched for potential and
dynamical potential algebras of the Smorodinsky-Winternitz system. The action
of generators on wavefunctions is given in explicit form for D=2.
