Relational memory is the ability to flexibly organize and integrate multiple sources of information to produce emergent outcomes. In tests for one type of relational memorystimulus equivalence-arbitrary stimuli become related in ways not explicitly trained. Little is known however about whether stimulus equivalence-based relational memory ability differentially emerges during offline periods of either sleep or wake. Here, fifty-one, healthy young adults learned a series of interconnected conditional relations involving arbitrary visual images (A-B, A-C, and AD), and were immediately tested for maintenance of these relations. Following a 12-hour offline period consisting of either sleep or wake, both groups were tested for novel inferences-symmetry (B-A, C-A, and D-A) and equivalence relations (B-C, C-B, C-D, and D-C)-as well as retention of the trained relations. Results from delayed testing, supported by Bayesian statistics, showed that accuracy did not differ between the sleep and wake groups. Potential limitations of this preliminary investigation and directions for future research are discussed.