We show that classical localization occurs for the drift - diffusion equation on an ordered Cayley tree when the drift velocity v on each branch of the tree exceeds a critical value , where z is the coordination number, D is the diffusion constant and L is the segment length. For the asymptotic decay of the delocalized state exhibits conventional diffusive behaviour, whereas at the critical point there is anomalous behaviour in the form of a critical slowing-down. A necessary condition for localization in the presence of randomly distributed drift velocities is also derived.