In the control problems of modern dynamic objects, the control action is formed not by the state vector, but by the output variable, the dimension of which is much smaller. Missing information is restored using asymptotic observers. Therefore, the task of their synthesis, especially for nonlinear systems, seems quite relevant. The article considers nonlinear models of a special form and the formulation of the synthesis problem for a nonlinear asymptotic observer for them. Sufficient conditions that guarantee the asymptotic stability of the zero equilibrium of the observation error are also presented. A numerical solution of the problem for a two-link robotic system is given for various parameter values as an example.