Strong sustainability, according to the common definition, requires that different natural and economic capital stocks have to be maintained as physical quantities separately. Yet, in a world of uncertainty this cannot be guaranteed. To therefore define strong sustainability under uncertainty in an operational manner, we propose to use the concept of viability. Viability means that the different components and functions of a dynamic, stochastic system at any time remain in a domain where the future existence of these components and functions is guaranteed with sufficiently high probability. We develop a unifying and general ecological-economic concept of viability that encompasses the traditional ecological and economic notions of viability as special cases. It provides an operational criterion of strong sustainability under conditions of uncertainty. We illustrate this concept and demonstrate its usefulness by applying it to livestock grazing management in semi-arid rangelands.