In higher-order four period crossover designs with two treatments, sixteen possible treatment sequences can result: AAAA, AAAB, AABA, AABB, ABAA, ABAB, ABBA, ABBB and their duals. Higher-order crossover designs are useful for several reasons: they allow estimation of a treatment effect even in the presence of a carry-over effect, they provide estimates of intra-subject variability and they draw inference on the carry-over effect. The real question related to a two-treatment four-period crossover design is the real world application of these designs. This article considers four designs: Design I: ABBA and its dual; Design II: ABBA, AABB and their duals, Design III: ABBA, ABAA and their duals, Design IV: ABBA, ABAB and their duals. A traditional model that specifies a first-order carryover effect is assumed and methods for estimating treatment and first-order carryover effects in the set of four period trials are outlined.