This paper develops a new class of measures of mobility as an equalizer of longer-term incomes – a concept different from other notions such as mobility as time-independence, positional movement, share movement, income flux, and directional income movement. A number of properties are specified leading to a class of indices, one easily-implementable member of which is applied to data for the United States and France. Using this index, income mobility is found to have equalized longer-term earnings among U.S. men in the 1970s but not in the 1980s or 1990s. In France, though, income mobility was equalizing throughout, and it has attained its maximum in the most recent period.