We review the geodesic motion of pseudo-classical spinning particles in
curved spaces. Investigating the generalized Killing equations for spinning
spaces, we express the constants of motion in terms of Killing-Yano tensors.
The general results are applied to the case of the four-dimensional Euclidean
Taub-NUT spinning space. A simple exact solution, corresponding to trajectories
lying on a cone, is given.Comment: 33 pages, LaTeX2e, to appear in Fortschritte der Physi