We have observed both peaks and troughs in the magnetoresistance of organic nanowires consisting of three layers—cobalt, 8-hydroxy-quinolinolato aluminum (Alq3), and nickel. They always occur between the coercive fields of the ferromagnetic layers, and we attribute them to the normal and inverse spin-valve effect. The latter is caused by resonant tunneling through localized impurity states in the organic material. Peaks are always found to be accompanied by a positive monotonic background magnetoresistance, while troughs are accompanied by a negative monotonic background magnetoresistance. This curious correlation suggests that the background magnetoresistance, whose origin has hitherto remained unexplained, is probably caused by the recent...