A nonparametric method of modeling respiratory mechanics and gas exchange is presented and compared to existing parametric methods. The nonparametric approach is based on Wiener's theory of nonlinear system identification by use of white-noise test inputs. The sought nonparametric models have the form of nonlinear functional relations between tracheal pressure and flow (in the study of respiratory mechanics), and between tracheal flow and PCO2 (in the study of gas exchange). The motivation for this modeling study is provided by the recent emergence of high-frequency ventilation as a useful clinical tool. The obtained results increase our understanding of the quantitative relations between these physiological variables, and allow optimization studies that may lead to improved clinical applications.