The structural behaviour of the orthorhombic multi-il-alkane crystalline beta＇ phase, observed in mixtures consisting of 23 (19 < n < 43) and 33 (19 < n < 53) n-alkanes respectively, is studied by X-ray diffraction with increasing temperature. A Rotator single-phase domain of rhombohedral (or hexagonal) alpha-RII type is observed below the solidus point. The product, consisting of 23 n-alkanes, undergoes this structural transition (beta＇ --> alpha-RII) through two two-phase domains: first, a region with the beta＇ and beta(Fmmm) phases; then, a domain with the two beta(Fmmm)-RI and alpha((R (3) over bar m)-RII Rotator phases. For two beta＇ solid solutions consisting of 33 n-alkanes, a single two-phase domain (beta＇ + alpha-RII) is observed in the course of this structural crystal-Rotator transition.