We discuss combinatorial properties of a class of binary sequences generalizing Sturmian sequences and obtained as a coding of an irrational rotation on the circle with respect to a partition in two intervals. We give a characterization of those having a finite index in terms of their ${\cal D}$-expansion. Then, we deal with powers occurring at the begining of these words and we prove, contrary to the Sturmian case, the existence of such sequences without any asymptotic initial power. We keep on this study by showing that all charateristic sequences have even so almost initial powers and we apply this property to obtain the transcendence of associated continued fractions.