  The problem of the characterization of all analytic potentials which give
rise to isochronous oscillatory motions still open. However, there are several
approaches to highlight motions with period $T(E) \equiv T_0$ independent on
the energy. It is proposed in this paper to give necessary and sufficient
conditions for a center to be isochronous. The proofs produced here are self
contained. As corollaries we find again lot of known conditions previously
established by different authors. This allows us to produce several class of
isochronous analytic motions. We are also interested in the quantum spectrum.
We then use the perturbation method WKB to derive an expression for the
corrections to the equally spaced valid for analytic isochronous potentials.
