Among all catacondensed benzenoid molecules the unbranched systems possess the largest number of spanning trees. Some other relations for the spanning-tree count of catacondensed benzenoids are also reported. The results obtained continue to hold for catacondensed molecules composed of rings the size of which differ from six. The propositions reported do, however, depend for their validity on there being rings of only one size in the catacondensed system under study.