Resilience as a descriptive concept gives insight into the dynamic properties of a system. Sustainability as a normative concept captures basic ideas of inter- and intragenerational justice. In this paper we specify the relationship between resilience and sustainable development. Based on an ecological-economic model where two natural capital stocks provide ecosystem services that are complements for human well-being, we derive conditions on the dynamics of the ecological-economic system and the sustainability criterion, such that a) resilience of the system in a given regime is both necessary and sufficient for sustainable development, b) resilience of the system in a given regime is sufficient, but not necessary, c) resilience of the system in a given regime is necessary, but not sufficient, and d) resilience of the system in a given regime is neither necessary nor sufficient for sustainable development. We conclude that more criteria than the resilience of the current state of the system have to be taken into account when designing policies for sustainable management of ecological-economic systems.