The concept of quasilocal (F, C, D) correction of nonlinearities is reviewed. Correction by two or more orders of magnitude is obtained; in addition, separated‐function control of the horizontal, coupled and vertical motion becomes possible. Quasi‐local correction of dipole nonlinearities is planned for LHC, and will greatly increase the linear aperture. The 1990 SSC Site‐Specific Conceptual Design includes quasilocal correction in the 20 TeV Collider, but restrictions may limit correction capability. Quasilocal (F, C, D) correction may also be useful in the SSC 2‐TeV High Energy Booster (HEB). In high‐luminosity collider mode, the nonlinear effects of the interaction‐region (IR) quadrupoles may be dominant; these errors may also be compensated quasilocally. Extensions of the (F, C, D) concept for IR correction, which exploit the restricted IR symmetry, are also suggested.