  We formulate the necessary conditions for the maximal super-integrability of
a certain family of classical potentials defined in the constant curvature
two-dimensional spaces. We give examples of homogeneous potentials of degree -2
on $E^2$ as well as their equivalents on $S^2$ and $H^2$ for which these
necessary conditions are also sufficient. We show explicit forms of the
additional first integrals which always can be chosen polynomial with respect
to the momenta and which can be of an arbitrary high degree with respect to the
momenta.
