  Hidden symmetries of generalized Kaluza-Klein-type metrics are studied using
van Holten's systematic analysis \cite{vH} based on Killing tensors. Applied to
generalized Taub-NUT metrics, Kepler-type symmetries with associated
Runge-Lenz-type conserved quantities are constructed. In the multicenter case,
the subclass of two-center metrics gives rise to a conserved Runge-Lenz-type
scalar, while no Kepler-type constant of the motion does exist for non aligned
$(N\geq3)$-centers. We also investigated the diatomic molecule system of
Wilczek et al. where "truly" non-Abelian gauge fields mimicking monopole-like
fields arised. From the latter system we deduced a new conserved charge.
