Two Mg–4Li–xY (x = 0.5 and 2.0 wt%) alloy wires are investigated for application in bioresorbable medical devices that experience high levels of plastic deformation. The two wires are supplied cold drawn to a diameter of 125 μm, and a series of thermal treatments are applied to maximize ductility. The ductility of the alloys is maximized soon after complete recrystallization. Prolonged annealing causes grain coarsening in the Mg–4Li–0.5Y alloy and precipitation of a Mg24Y5 phase in both alloys. Both wires are shown to achieve ≈20% elongation to failure in tension and survive high idealized bending strains (>40%). When heat treated for optimum mechanical properties for the intended application, the Mg–4Li–0.5Y alloy develops an intense transverse basal texture; however, this is shown to weaken with increased Y content in the Mg–4Li–2Y alloy wire. The increased Y content also prevents grain coarsening, indicating that the increased Y content restricts grain boundary mobility during annealing. Both alloys have relatively high ductility, meaning both are identified as promising new materials for application in bioresorbable medical devices that require to achieve and support high levels of plastic deformation during their life cycle.