The main objective of the BALGIM océanographie cruise (R.V. "Cryos", 25.05-22.06.1984) was to investigate the faunal exchanges between the Atlantic Ocean and the Mediterranean Sea. The present paper, first of three devoted to Bryozoa, deals with the chéilostomes (115 species) collected in the Gulf of Cadiz, the Strait of Gibraltar and the Alboran Sea (115-1917 m). The morphological features and the taxonomic status of 26 species are discussed. Two new genera (Clavodesia, Sertulipora), three new species (Hincksina longispinosa, Clavodesia biradiculata, Sertulipora guttata) and two new subspecies (Phylactella labrosa tangerina, Schizomavella linearis profunda) are described.