Viscous remanent magnetization (VRM) generated during the Brunhes epoch is a major source of paleomagnetic noise. VRM is usually 'soft' or easily erased by alternating field (af) demagnetization, but we find that in a few hour's exposure to a weak field, hematite grains 0.1--5 &mgr;m in size acquire significant VRM, about 10% of which survives af demagnetization to 400 Oe. The finer the grains and the longer the exposure time, the more intense and resistant to demagnetization VRM. Calculations using the N¿el [1949> single-domain theory of VRM indicate that 'hard' VRM is not confined to hematite. It is a property of fine grains of any highly coercive magnetic mineral, e.g., elongated single-domain grains of iron in lunar rocks. In terrestrial hematite-bearing rocks, e.g., red beds, VRM acquired over the Brunhes epoch is probably largely unaffected by routine af demagnetization. However, these rocks can be successfully cleaned by heating because 'hard' VRM is 'soft' to thermal demagnetization.