While tropical cyclone (TC) track forecasts have become increasingly accurate over recent decades, intensity forecasts from both numerical models and statistical schemes have been trailing behind. Most operational statistical–dynamical forecasts of TC intensity use linear regression to relate the initial TC characteristics and most relevant large-scale environmental parameters along the TC track to the TC intensification rate. Yet, many physical processes involved in TC intensification are nonlinear, hence potentially hindering the skill of those linear schemes. Here, we develop two nonlinear TC intensity hindcast schemes, for the first time globally. These schemes are based on either support vector machine (SVM) or artificial neural network (ANN) algorithms. Contrary to linear schemes, which perform slightly better when trained individually over each TC basin, nonlinear methods perform best when trained globally. Globally trained nonlinear schemes improve TC intensity hindcasts relative to regionally trained linear schemes in all TC-prone basins, especially the SVM scheme for which this improvement reaches ;10% globally. The SVM scheme, in particular, partially corrects the tendency of the linear scheme to underperform for moderate intensity (category 2 and less on the Saffir–Simpson scale) and decaying TCs. Although the TC intensity hindcast skill improvements described above are an upper limit of what could be achieved operationally (when using forecasted TC tracks and environmental parameters), it is comparable to that achieved by operational forecasts over the last 20 years. This improvement is sufficiently large to motivate more testing of nonlinear methods for statistical TC intensity prediction at operational centers.