Alternans of cardiac repolarization is associated with arrhythmias and sudden death. At the cellular level, alternans involves beat-to-beat oscillation of the action potential (AP) and possibly Ca²⁺ transient (CaT). Because of experimental difficulty in independently controlling the Ca²⁺ and electrical subsystems, mathematical modelling provides additional insights into mechanisms and causality. Pacing protocols were conducted in a canine ventricular myocyte model with the following results: (I) CaT alternans results from refractoriness of the SR Ca²⁺ release system; alternation of the L-type Ca²⁺ current (I_Ca(L)) has a negligible effect; (II) CaT-AP coupling during late AP occurs through the Na⁺/Ca²⁺ exchanger (I_NaCa) and underlies APD alternans; (III) Increased Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) activity extends the range of CaT and APD alternans to slower frequencies and increases alternans magnitude; its decrease suppresses CaT and APD alternans, exerting an antiarrhythmic effect; (IV). Increase of the rapid delayed rectifier current (I_Kr) also suppresses APD alternans, but without suppressing CaT alternans. Thus, CaMKII inhibition eliminates APD alternans by eliminating its cause (CaT alternans), while I_Krenhancement does so by weakening CaT-APD coupling. The simulations identify combined CaMKII inhibition and I_Kr enhancement as a possible antiarrhythmic intervention.