"Melkites" is a common label, in the medieval world of Islam, for Christians adhering to the (Chalcedonian) faith of the Byzantines. Defined by their theological profile, the Melkites also form a Church: it is from an institutional point of view that this dissertation studies their history, in Syria and Palestine, during the transition from Byzantium to Islam. While relying on a wide range of sources, the research focuses on a dossier of Church documents in Arabic issued in the late 9th century, in the course of a conflict involving David, metropolitan bishop of Damascus, and concerning the administration of its churches. Edition and French translation of this dossier are provided as an appendix. Two aspects of the history of the Melkite Church are studied: its ecclesiastical hierarchy and geography between 600 and 969, and the government of the Church through its administration. The dissertation offers a revision of the chronology of the patriarchs, an inventory of the post-Byzantine episcopal hierarchy and a discussion on the place of monasteries in the Melkite Church. The administration of worship and church property can occasionally be grasped, at the local level of the city, according to a nomenclature largely inherited from the Byzantine period, but behind which new issues such as the tax burden may be detected. The handwritten material, especially canonical documentation, provides insights into the judicial process, conflict resolution and legal practices within the Melkite Church. In a transversal way, the issue of authority in the Church and the construction of institutional memory help to think about the social significance of the ecclesial institution.