Summary: First-order sensitivity analysis cannot accurately characterize the nonlinear behavior in atmospheric response. To alleviate this limitation, the decoupled direct method (DDM) is extended to calculate higher-order sensitivity coefficients. High-order DDM (HDDM) is very efficient and calculates sensitivity coefficients of different orders at approximately the same computational cost as the first-order calculations. By applying higher-order analysis, a more accurate prediction of the response is achieved when nonlinearity is present. Some of the most nonlinear behaviors (largest magnitudes of high-order sensitivity coefficients) are seen in the high ozone concentration areas downwind of urban or industrial emissions. Applying high-order analysis in developing control strategies for such cases will result in markedly improved accuracy when assessing the response to large changes in emissions. Also, by using HHDM in calculation of the cross-derivatives (sensitivity to two or more parameters), the time-dependent and location-specific ozone isopleths are developed for a photochemical episode. Finally, by applying HDDM to reactivity simulations of central California, local uncertainty analysis of 3-D organic reactivities is carried out for six species and 27 uncertain inputs and parameters. As expected, the relative reactivities are found to have significantly lower uncertainty than the absolute values. Uncertainty contributions from different input parameters show a great deal of spatial variation and largely depend on the prevailng chemical environment. In general, uncertainty levels in relative reactivities are low-to-moderate (10--50%) and reaffirm the conclusion that the relative reactivity scales can be used reliably for VOC control regulations.