Traditional maintenance decisions in the framework of condition-based maintenance applied to multi-component systems are performed either at the system level or at the component level. These decisions however cannot always assure the best maintenance performance. To remedy this drawback, the present paper introduces a multi-level decision-making approach that combines maintenance decisions at the system level and the component level. The effectiveness of such an approach is investigated through an n-component deteriorating system with a k-out-of- n:F structure, and economic dependence. In fact, based on the degradation and failure model of the considered k-out-of- n:F system, two new opportunistic predictive maintenance strategies with different types of maintenance decision-making are proposed. In the first one, the decisions rely only on the remaining useful lifetime of the components; while in the second one, they are based on both the remaining useful lifetimes of the system and that of its components. The maintenance cost models of these strategies are developed on the basis of semi-regenerative theory, optimized, and then compared with each other. The comparison results show that the multi-level decision-making approach allows us to more effectively avoid inopportune interventions, to better take into account the interactions among components, and hence to provide more flexible and profitable predictive maintenance strategies for multi-component systems.