Nineteen pillow basalts dredged within the rift valley of the Mid-Atlantic Ridge at 36.8oN were studied by the Thellier stepwise heating method in order to determine the paleointensity of the geomagnetic field when they erupted on to the sea floor. Previously reported fission track ages are 2000-6000 yr for the youngest rocks (mainly olivine basalts) and 10 000-100 000 yr for the others (mainly plagioclase basalts and pyroxene basalts). All but three pillow basalts meet the conditions commonly considered as indicative of quite reliable paleointensity estimates; stability of the direction of NRM during its thermal demagnetization, constant ratio of NRM/TRM (natural remanent magnetization to thermoremanent magnetization) over 50% or more of the original NRM intensity (80 to 94% for 11 specimens), and reproducibility of low-temperature partial TRM(PTRM). However, strong field thermomagnetic measurements indicate that 11 of these 16 samples display a significant increase in Curie temperature (15 to 80oC) during the paleointensity experiments below 250oC, notwithstanding the linearity of the NRM-TRM plot in this temperature interval. This alteration, probably due to low-temperature oxidation of the specimens, seems typical of young pillow basalts and may result in paleointensity estimates which are too high.-from Authors