[en] New methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron are presented and discussed. In a simplest form, correction elements are placed at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's Rule. The F, C, and D correctors also permit direct control of horizontal, coupled, and vertical motion. For example, second-order sextupole nonlinearities can be corrected with F, C, and D octupoles. Generalizations and variations of the methods are described and applications to the SSC, LHC, AHF, and HERA projects are discussed. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in synchrotrons are demonstrated. 13 refs., 2 figs., 1 tab