  We present the quadratic algebra of the generalized MICZ-Kepler system in
three-dimensional Euclidean space $E_{3}$ and its dual the four dimensional
singular oscillator in four-dimensional Euclidean space $E_{4}$. We present
their realization in terms of a deformed oscillator algebra using the
Daskaloyannis construction. The structure constants are in these cases function
not only of the Hamiltonian but also of other integrals commuting with all
generators of the quadratic algebra. We also present a new algebraic derivation
of the energy spectrum of the MICZ-Kepler system on the three sphere $S^{3}$
using a quadratic algebra. These results point out also that results and
explicit formula for structure functions obtained for quadratic, cubic and
higher order polynomial algebras in context of two-dimensional superintegrable
systems may be applied to superintegrable systems in higher dimensions with and
without monopoles.
