Reduced-order models are considered in the context of parameter adaptive controllers for tracking workspace trajectories. A dual-arm manipulation task is used to illustrate the methodology and provide simulation results. A parameter adaptive controller is designed to track a payload trajectory using a four-parameter model instead of the full-order, nine-parameter model. Several simulations with different payload-to-arm mass ratios are used to illustrate the capabilities of the reduced-order model in tracking the desired trajectory. The adaptive controller was able to reduce tracking errors substantially over the constant gain approach for cases where the payload began to dominate the system dynamics. This meant that even when only slight perturbations to the four-parameter model used by the controller were present, the adaptive controller could reduce the tracking errors significantly, as if a full-order model were being used.>