We introduce a new 2N--parametric family of maximally superintegrable systems
in N dimensions, obtained as a reduction of an anisotropic harmonic oscillator
in a 2N--dimensional configuration space. These systems possess closed bounded
orbits and integrals of motion which are polynomial in the momenta. They
generalize known examples of superintegrable models in the Euclidean plane.Comment: 6 pages. Version accepted in Physical Review