A method of asymptotic output tracking in a class of causal nonminimum-phase uncertain nonlinear systems is considered. Local asymptotic stability of output tracking-error dynamics are provided for the specified class of systems with the nonlinear hyperbolic at the origin internal dynamics forced by a reference output profile and external disturbances defined by a known linear exosystem. The nonlinear vector field of the internal dynamics is expanded in a power series, obtained at a selected operational point in the internal dynamics state space. The presented technique employs some linear algebraic methods and sliding mode control approach. The solution is a complete constructive algorithm.