A section at below 3.1 km depth in Icelandic crust, sampled in the 1978 Icelandic Research Drilling Project drill hole, contains a number of subaerially deposited lava flows showing both downwards and probably original upwards inclinations of cleaned, stable remanent magnetization. Such "mixed polarities" are inconsistent with an initial cooling thermoremanent origin for the magnetization. An attempt is made to identify the factors involved in producing these mixed polarities and to consider the possible wider importance of the results. The mixed-polarity flows have experienced intense hydrothermal alteration, followed by the widespread deposition of secondary magnetite. Secondary magnetite, which is formed in relatively anhydrous conditions associated with dike intrusion, dominates primary magnetite volumetrically where dike density locally exceeds about 30%.Where secondary magnetite is very dominant or is the only type of magnetite present, directional remagnetization appears to be uniform and complete. Where secondary and primary magnetite are both important, relatively high remanence and saturation magnetizations, total magnetite and primary magnetite grain size, and low deuteric oxidation state of primary magnetite are all associated with downwards directional remagnetization. It appears that a complex balance of the properties and history of primary and secondary magnetite, in addition to the relative abundances of these phases, controls the final stable polarity of samples.If the narrow transition zones between little-altered extrusives, greenschist-facies flows and dikes of the Troodos (Cyprus) ophiolite, and DSDP hole 504B are typical of oceanic crust, a narrow ~0.2 km interval of mixed polarities may be underlain in some locations by an intermediate crustal layer in polarity opposition with the uppermost, little-altered, extrusive layer.