A variety of equating methods based on icc theory are surveyed and compared with nonlinear conventional methods. In many cases, the icc model replaces a nonlinear equating problem by a linear one. This helps the stability of the equating near the extremes of the data. Strictly speaking, icc methods are the only methods appropriate when the tests to be equated are given (with an anchor test) to groups differing in ability. It seems likely that icc methods can reduce drift in equating chains involving many links. Research into the practical value of preequating is recommended. (37pp.)