The filamentous fungus Trichoderma reesei produces two cellobiohydrolases (CBHI and CBHII). These, like most other cellulose‐degrading enzymes, have a modular structure consisting of a catalytic domain linked to a cellulose‐binding domain (CBD). The isolated catalytic domains bind poorly to cellulose and have a much lower activity towards cellulose than the intact enzymes. For the CBDs, no function other than binding to cellulose has been found. We have previously described the reversibility and exchange rate for the binding of the CBD of CBHI to cellulose. In this work, we studied the binding of the CBD of CBHII and showed that it differs markedly from the behaviour of that of CBHI. The apparent binding affinities were similar, but the CBD of CBHII could not be dissociated from cellulose by buffer dilution and did not show a measurable exchange rate. However, desorption could be triggered by shifting the temperature. The CBD of CBHII bound reversibly to chitin. Two variants of the CBHII CBD were made, in which point mutations increased its similarity to the CBD of CBHI. Both variants were found to bind reversibly to cellulose.