A cruise carried out aboard the Spanish R/V Hesperides using a 255-inch(3) airgun allowed to identify three main seismostratigraphic units in the western submarine flanks of the islands of La Palma and El Hierro, Canary Islands. The time structure and thickness maps of each unit, together with the interpretation of the seismic facies, demonstrate that the evolution of the Canary Islands is recorded in the marine basin, The structure maps show that the older reflectors dip to the NW in contrast to the present-day sea floor which dips to the WNW. The thickness maps also show that the depocentre moved from a position parallel to the Northwest African margin to a position now occupied by the island of La Palma. Despite the high sedimentation rates of hemipelagic background sedimentation in the study area, the three seismic units can be interpreted in terms of their relation to the Canarian volcanism, Unit I was deposited before the initiation of volcanism and the arrival of volcaniclastic flows and is thus mainly, if not entirely, composed of hemipelagic sediments. Unit II seems to reflect the shield phases of the easternmost edifices, and as such would be constituted by the distal products of erosion and mass wasting of these islands. Unit III, in contrast, results mainly from the shield phase of the two westernmost islands (La Palma and El Hierro), and as such reflects more proximal conditions, as demonstrated by the presence of lateral collapse deposits from these islands. (C) 1998 Elsevier Science B.V. All rights reserved.