A control strategy for enabling a team of unmanned aircraft systems (UASs) to cooperatively transport a cable-suspended rigid-bodypayload of unknown characteristics is proposed. Considering the rigid-body payload as a disturbance with unmodeled dynamics affecting the aircraft, a fuzzy approximator is designed to identify the lumped disturbances existing in the system, which include also the forces of interaction between the aircraft. Next, a nonlinear controller is designed, which makes use of the approximator to compensate such disturbances. Making use of the fuzzy approximator and the nonlinear controller, a novel consensus-type strategy is proposed, enabling the load transportation task by means of two cooperative quad rotorcraft UASs. The stability of the proposed methodology is demonstrated making use of Lyapunov theory. The nonlinear consensus controller enhanced with fuzzy compensation is compared with respect to a feedback controller with feedforward compensation, demonstrating superior performance of the proposed technique in terms of robustness and stability. Experimental results demonstrate the applicability of the theoretical framework for executing the real-time transportation of a cable-suspended rigid-body payload by means of a team of two cooperative quad rotor UASs.