Musculoskeletal robots are a class of compliant, tendon-driven robots that can be used in robotics applications, as well as in the study of biological motor systems. Unfortunately, there is little progress in controlling such systems. The aim of this work is to apply modern non-linear control approaches to overcome the challenges posed by the muscle compliance, the multi-DoF joints, as well as unmodeled dynamic effects such as friction. Specifically, a controller is derived for a generic model of musculoskeletal robots utilizing a multidimensional form of Dynamic Surface Control (DSC), an extension to backstepping. Subsequently this controller is extended by an adaptive neural network to compensate for both muscle and joint friction. The developed controllers are evaluated against the state of the art Computed Force Control (CFC), an application of feedback linearization, on the reference model of a spherical joint which is actuated by five muscles.