The Decentralized Navigation Functions' ( DNF) based methodology, established in our previous work ( D. V. Dimarogonas, M. M. Zavlanos, S. G. Loizou and K. J. Kyriakopoulos, "Decentralized motion control of multiple holonomic agents under input constraints'', in 42nd IEEE Conf. Deci. Cont., 2003, pp. 3390 - 3395 and S. G. Loizou, D. V. Dimarogonas and K. J. Kyriakopoulos, "Decentralized feedback stabilization of multiple nonholonomic agents'', in 2004 IEEE Int. Conf. on Robotics and Autom., 2004, pp. 3012 - 3017) on multi-agent systems with kinematic models of motion, is extended to the case where dynamic models of motion for both holonomic and nonholonomic agents must be treated. The proposed control scheme guarantees collision avoidance and global convergence of the multi-agent team to the desired goal configuration. The volume of each agent is taken into account and non-point models are considered. The satisfaction of the imposed system specifications under the proposed control scheme are verified and depicted through non-trivial computer simulations.