ABSTRACTThe Layer Korringa Kohn Rostoker-Coherent Potential Approximation technique was used to calculate the low temperature Giant Magnetoresistance from first principles for Co|Cu and permalloy|Cu superlattices. Our calculations predict large giant Magnetoresis-tance ratios for Co|Cu and extremely large ratios for permalloy|Cu for current perpendicular to the layers. Mechanisms such as spin-orbit coupling which mix spin channels are expected to greatly reduce the GMR effect for permalloy|Cu.