  We study the conformal groups of Jordan algebras along the lines suggested by
Kantor. They provide a natural generalization of the concept of conformal
transformations that leave 2-angles invariant to spaces where "p-angles" can be
defined. We give an oscillator realization of the generalized conformal groups
of Jordan algebras and Jordan triple systems(JTS). These results are extended
to Jordan superalgebras and super JTS's. We give the conformal algebras of
simple Jordan algebras, hermitian JTS's and the simple Jordan superalgebras as
classified by Kac.
