Rotation samples are frequently used in continuing surveys in order to obtain estimates of changes in a characteristic over time as well as separate estimates of the characteristic at specific points in time. Rotation designs involve the retention of some sampling units and the replacement of others. It has been observed in some studies that there are systematic changes in the estimate of a characteristic, depending on the frequency of appearance of a rotation group in the sample. It is shown in this paper that these systematic changes must occur provided (1) the probability of a selected unit actually appearing in the sample is monotonically related to the characteristic under measurement, and (2) the probability of a selected unit actually appearing in the sample changes monotonically from one observation point to the next. Some numerical examples showing the form and magnitude of the potential biases are included.