As one common precursor for both PM 2.5 and O 3 pollution, NO x gains great attention because its controls can be beneficial for reducing both PM 2.5 and O 3 . However, the effectiveness of NO x controls for reducing PM 2.5 and O 3 are largely influenced by the ambient levels of NH 3 and VOC, exhibiting strong nonlinearities characterized as NH 3 -limited/NH 3 -poor and NO x -/VOC-limited conditions, respectively. Quantification of such nonlinearities is a prerequisite for making suitable policy decisions but limitations of existing methods were recognized. In this study, a new method was developed by fitting multiple simulations of a chemical transport model (i.e., Community Multiscale Air Quality Modeling System, CMAQ) with a set of polynomial functions (denoted as pf-RSM) to quantify responses of ambient PM 2.5 and O 3 concentrations to changes in precursor emissions. The accuracy of the pf-RSM is carefully examined to meet the criteria of a mean normalized error within 2 % and a maximal normalized error within 10 % by using 40 training samples with marginal processing. An advantage of the pf-RSM method is that the nonlinearity in PM 2.5 and O 3 responses to precursor emission changes can be characterized by quantitative indicators, including (1) a peak ratio (denoted as PR) representing VOC-limited or NO x -limited conditions, (2) a suggested ratio of VOC reduction to NO x reduction to avoid increasing O 3 under VOC-limited conditions, (3) a flex ratio (denoted as FR) representing NH 3 -poor or NH 3 -rich conditions, and (4) enhanced benefits in PM 2.5 reductions from simultaneous reduction of NH 3 with the same reduction rate of NO x . A case study in the Beijing–Tianjin–Hebei region suggested that most urban areas present strong VOC-limited conditions with a PR from 0.4 to 0.8 in July, implying that the NO x emission reduction rate needs to be greater than 20–60 % to pass the transition from VOC-limited to NO x -limited conditions. A simultaneous VOC control (the ratio of VOC reduction to NO x reduction is about 0.5–1.2) can avoid increasing O 3 during the transition. For PM 2.5 , most urban areas present strong NH 3 -rich conditions with a PR from 0.75 to 0.95, implying that NH 3 is sufficiently abundant to neutralize extra nitric acid produced by an additional 5–35 % of NO x emissions. Enhanced benefits in PM 2.5 reductions from simultaneous reduction of NH 3 were estimated to be 0.04–0.15 µg m −3 PM 2.5 per 1 % reduction of NH 3 along with NO x , with greater benefits in July when the NH 3 -rich conditions are not as strong as in January. Thus, the newly developed pf-RSM model has successfully quantified the enhanced effectiveness of NO x control, and simultaneous reduction of VOC and NH 3 with NO x can assure the control effectiveness of PM 2.5 and O 3 .