This study investigates the hypothesis of a nonlinear relationship between aggregate demand and inflation in the Russian economy. To detect the nonlinear effect, the aggregated Consumer Price Index was decomposed into cyclical (more sensitive to aggregate demand) and acyclical (less sensitive to aggregate demand) components. The decomposition methodology employed in the paper reveals a stable nonlinear link between aggregate demand and inflation. It is shown that the slope of the Phillips curve becomes significantly steeper, i.e., the sensitivity of inflation to economic activity increases, when two conditions are met simultaneously: 1) current general price growth rates exceed long-term inflation expectations; 2) the output gap is positive. Furthermore, it is established that the use of a nonlinear Phillips curve can significantly improve forecast accuracy if a preliminary decomposition of the CPI into cyclical and acyclical components is performed. The forecasting accuracy is asymmetric: inflation forecasts derived from Phillips curves (both linear and nonlinear) demonstrate higher precision during crisis periods. The obtained result proves robust to changes in the trend estimation method, alterations in the nonlinearity condition (using only a positive output gap), the exclusion of sharp CPI changes from the sample, and shifts in the left and right boundaries of the sample. The robustness of the result is also demonstrated with respect to the shock control procedure used in CPI decomposition: even without this procedure, the ability to detect the nonlinear relationship and the improved forecast accuracy (at least at the 9- to 12-month horizon) are preserved.