In this study, a PID type controller incorporating an adaptive control scheme for the mixed H-2/H-infinity tracking performance is developed for constrained non-holonomic mechanical systems under unknown or uncertain plant parameters and external disturbances. By virtue of the skew-symmetric property of the non-holonomic mechanical systems and an adequate choice of a state variable transformation, sufficient conditions are developed for the adaptive mixed H-2/H-infinity tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled non-linear differential equations. The coupled algebraic equations can be solved analytically. (C) 2003 Elsevier Science Ltd. All rights reserved.