  For each simple euclidean Jordan algebra $V$, we introduce the analogue of
hamiltonian, angular momentum and Laplace-Runge-Lenz vector in the Kepler
problem. Being referred to as the universal hamiltonian, universal angular
momentum and universal Laplace-Runge-Lenz vector respectively, they are
elements in (essentially) the TKK (Tits-Kantor-Koecher) algebra of $V$ and
satisfy commutation relations similar to the ones for the hamiltonian, angular
momentum and Laplace-Runge-Lenz vector in the Kepler problem. We also give some
examples of Poisson realization of the TKK algebra, along with the resulting
classical generalized Kepler problems. For the simplest simple euclidean Jordan
algebra (i.e., $\mathbb R$), we give examples of operator realization for the
TKK algebra, along with the resulting quantum generalized Kepler problems.
