PERIDOTITES found on the sea floor are widely believed to be residues left by mid-ocean-ridge basalt (MORB) melting. As such, their composition should provide insights into the nature of the sub-oceanic depleted mantle. But although these abyssal peridotites occur in mid-ocean ridge fracture zones(1,2), there is little other evidence in support of their genetic link with MORB, and doubts about it have been raised(3-5). Radiogenic isotopes should be able to provide a powerful test of the hypothesis, but previous studies(3,8-10) on whole rocks have not provided unambiguous answers as they are generally altered by sea water. Here we present measurements of the Nd and Sr isotope compositions of a suite of abyssal peridotite clinopyroxenes which should have resisted alteration. Despite residual seawater contamination of Sr in the clinopyroxenes, the data demonstrate that the peridotites are from a depleted mantle source, identical to that of MORB. This provides a strong indication that abyssal peridotites are residues of MORB melting.