This work investigates the identifiability and observability of two nonlinear wind turbine models. Various definitions of both concepts are summarized together with an interpretation of their relation. An overview of existing methods to assess the identifiability and observability of nonlinear systems qualitatively as well as quantitatively is given. Of these, the profile likelihood approach is chosen and applied to both models. Thereby, statistical confidence intervals for parameters and states are derived. The identifiability of the air density, eigenfrequency and wind velocity as well as the observability of all states is assessed for various wind scenarios and measurement configurations. A qualitative overview is given together with a detailed analysis for selected constellations. Furthermore, the validity of the used methodology is verified.