Single-asperity wear measurements were performed on small quantities of polyethylene with different molecular weights. Experiments could be performed on a surface area of 25 x 3000 mum(2). A quantitative value of wear rate could be obtained that was proportional to macroscopic results relating the wear rate to the molecular weight. Material transfer limited the maximum sliding velocity to 1 mum (.) s(-1). Possible solutions for this problem have been identified and will be a subject of further investigation.