From a consistent expression for the quadriforce describing the interaction between a colored particle and gauge fields, we investigate the relativistic motion of a particle with isospin interacting with a BPS monopole and with a Julia-Zee dyon. The analysis of such systems reveals the existence of unidimensional unbounded motion and asymptotic trajectories restricted to conical surfaces, which resembles the equivalent case of electromagnetism. (c) 2005 Elsevier B.V. All rights reserved.341417302232