A dual neural network is presented for the bi-criteria kinematic control of redundant manipulators. To diminish the discontinuity of minimum infinity-norm solutions, the kinematic-control problem is formulated in the bi-criteria of the infinity and Euclidean norms. Physical constraints such as joint limits and joint velocity limits are also incorporated simultaneously into the proposed kinematic control scheme. The single-layer dual neural network model with a simple structure is developed for bi-criteria redundant resolution of redundant manipulators subject to robot physical constraints. The dual neural network is shown to be globally convergent to optimal solutions in the bi-criteria sense, and is demonstrated to be effective in controlling the PA10 robot manipulator.