We describe herein biocompatible single crystal Cu-based shape memory alloys (SMAs). In particular, we show biocompatibility based on MEM elution cell cytotoxicity, ISO intramuscular implant, and hemo-compatibility tests producing negative cytotoxic results. This biocompatibility may be attributed to the formation of a durable oxide surface layer analogous to the titanium oxide layer that inhibits body fluid reaction to titanium nickel alloys, and/or the non-existence of crystal domain boundaries may inhibit corrosive chemical attack. Methods for controlling the formation of the protective aluminum oxide layer are also described, as are devices including such biocompatible single crystal copper-based SMAs.