This paper deals with the output tracking control of gear transmission servo (GTS) systems in the presence of deadzone nonlinearity with nonsymmetric beak points and unknown parameters. A novel differentiable deadzone model with nonsymmetric break points is put forward, which greatly facilitates the control design for a class of mechanical systems in the presence of deadzone nonlinearity. A new smooth backstepping controller, based on the newly-developed model, is proposed for the nominal system. Then, guaranteed robust steady-state performance of the closed-loop system with parametric uncertainties is derived by using Lyapunov analysis for the perturbed nonlinear systems. Simulations are carried out to validate the proposed algorithm and analysis in this paper.