Some properties of the 2-period change-over design are investigated. It is shown that if the effect of subjects is assumed to be a random variable, the difference between the direct effects and the difference between the residual effects of treatments are estimable, but the difference between periods is not. The amount of experimentation necessary to achieve a specified power of the test of equality of the direct effect of treatments resulting from a 2-period change-over design is compared to the amount required for a design in which the subjects are assigned randomly to a single treatment. This comparison shows that the 2-period change-over design is preferable when the residual effects of the treatments are equal and the correlation between the responses to the 2 treatments is positive. Otherwise a design in which each subject is assigned randomly to only 1 of the treatments is preferable.