Resilience as a descriptive concept gives insight into the dynamic properties of an ecological-economic system. Sustainability as a normative concept captures basic ideas of intergenerational justice when human well-being depends on natural capital and services. Thus, resilience and sustainability are independent concepts. In this paper, we discuss the relationship between resilience and sustainability of ecological-economic systems. We use a simple dynamic model where two natural capital stocks provide ecosystem services that are complements for human well-being, to illustrate different possible cases of the relationship between resilience and sustainability, and to identify the conditions under which each of those will hold: a) resilience of the system is necessary, but not sufficient, for sustainability; b) resilience of the system is sufficient, but not necessary, for sustainability; c) resilience of the system is neither necessary nor sufficient for sustainability; and d) resilience is both necessary and sufficient for sustainability. We conclude that more criteria than just resilience have to be taken into account when designing policies for the sustainable development of ecological-economic systems, and, vice versa, the property of resilience should not be confused with the positive normative connotations of sustainability.