We present measurements of the rotation rates of individual starspots on the rapidly rotating young K0 dwarf AB Doradus, at six epochs between 1988 December and 1996 December. The equatorial rotation period of the star decreased from 0.5137 to 0.5129 days between 1988 December and 1992 January. It then increased steadily, attaining a value of 0.5133 days by 1996 December. The latitude dependence of the rotation rate mirrored the changes in the equatorial rotation rate. The beat period between the equatorial and polar rotation periods dropped from 140 days to 70 days initially, then rose steadily. The most rigid rotation, in 1988 December, occurred when the starspot coverage was at a maximum. The time-dependent part of the differential rotation is found to have Delta Omega / Omega ~ 0.004, which should alter the oblateness of the star enough to explain the period changes observed in several close binaries via the mechanism of Applegate (1992).