  van Holten's algorithm is used to construct Runge-Lenz-type conserved
quantities, induced by Killing tensors, on curved manifolds. For the
generalized Taub-NUT metric, the most general external potential such that the
combined system admits a conserved Runge-Lenz-type vector is found. In the
multi-center case, the subclass of two-center metric exhibits a conserved
Runge-Lenz-type scalar.
