This paper presents the design and evaluation of a nonlinear control scheme for multirotor helicopters that takes first-order drag effects into account explicitly. A dynamic model including the blade flapping and induced drag forces is presented. Based on this model, a hierarchical nonlinear controller is designed to actively compensates for the nonlinear effects these drag forces. Reported simulation and experimental results indicate the significant performance improvement of the proposed drag-augmented control scheme with respect to a conventional nonlinear controller. For completeness, an offline procedure allowing for efficiently identifying the drag parameters is proposed.