New dideoxy- and 2'-deoxy-carbocyclic nucleosides built on a bicyclo[3.1.0]hexane template were synthesized and evaluated for antitumor and antiviral activity. The 4',6'-methano [3.1.0]bicyclic compounds possess a rigid pseudosugar conformation in the northern hemisphere of the pseudorotation cycle, while the 1',6'-methano [3.1.0]bicyclics, on the other hand, possess a rigid pseudosugar conformation in the southern hemisphere. These conformations have been ascertained by NMR spectroscopy.