It is shown that the current-perpendicular-to-plane giant-magnetoresistance (CPP-GMR) oscillations, in the ballistic regime, are strongly correlated with those of the exchange coupling (J). Both the GMR and J are treated on an equal footing within a rigorously solvable tight-binding single-band model. The strong correlation consists in an asymptotic sharing of the same period, determined by the Fermi surface, and oscillations with varying spacer thickness predominantly in opposite phases.