Adhesion was measured repeatedly between opposed molecularly thin layers of perfluoropoly(alkyl ether)s on mica, with particular attention to the dependence of the adhesion on chain-end functionality and chain length of the polymer. The polymer layers were kept in contact for specified times that differed by 4 orders of magnitude (0.01-500 s) and then unloaded (separated) at rates that varied by 5 orders of magnitude (0.003-120 mu m/s of a detachment device with spring constant 1.1 x 10(4) N/m) using a modified surface forces apparatus with piezoelectric actuators supporting one surface. Rate dependence resulting in an increase of the adhesion by a factor up to 3 was observed when the unloading rate exceeded a critical value that was found to depend not only on the polymer sample but also on the contact time between opposed layers. At a given unloading rate, the adhesion was larger, the longer the surfaces were left in stationary contact before separation. No history dependence was observed when the unloading rate was raised and subsequently lowered. For relatively short contact times (0.01-1 a), the critical unloading rate was larger for the polymer that contained polar end groups than for unfunctionalized polymer of similar chain length, indicating a lower mobility in the former case, and thus slower initial interdigitation of the chains, since the polar end group had a preferential affinity for the underlying surface. This effect vanished for contact times of 100-500 s. For polymer chains without polar end groups, the critical value of the unloading rate was smaller, the larger the chain length, and the increase in adhesion with unloading rate was more pronounced, presumably reflecting slower relaxation of the longer chains. The rate dependence is analyzed quantitatively.