Artificial intelligence (AI) systems are increasingly filling social roles traditionally filled by humans, raising questions about whether people apply the same relational norms to human-AI interactions as they do to human-human ones. To investigate this, we surveyed a gender-representative sample of U.S. adults (N = 432) on their expectations regarding four categories of relational norms—care, hierarchy, transaction, and mating—across seven types of relationships (i.e., fellow workers, supervisor-assistant, teacher-student, mental health provider-patient, customer-seller, long-term romantic partners, close friends). Depending on condition, we described these relationships as consisting of either of two humans or one human and a superintelligent AI. Participants then rated the extent to which each party in the relationship should—or should not—behave in a manner consistent with care, hierarchy, transaction, and mating.