It is evident when the resilience of a system has been exceeded and the system qualitatively changed. However, it is not clear how to measure resilience in a system prior to the demonstration that the capacity for resilient response has been exceeded. We argue that self-organizing human and natural systems are structured by a relatively small set of processes operating across scales in time and space. These structuring processes should generate a discontinuous distribution of structures and frequencies, where discontinuities mark the transition from one scale to another. Resilience is not driven by the identity of elements of a system, but rather by the functions those elements provide, and their distribution within and across scales. A self-organizing system that is resilient should maintain patterns of function within and across scales despite the turnover of specific elements (for example, species, cities). However, the loss of functions, or a decrease in functional representation at certain scales will decrease system resilience. It follows that some distributions of function should be more resilient than others. We propose that the determination of discontinuities, and the quantification of function both within and across scales, produce relative measures of resilience in ecological and other systems. We describe a set of methods to assess the relative resilience of a system based upon the determination of discontinuities and the quantification of the distribution of functions in relation to those discontinuities. ?? 2005 Springer Science+Business Media, Inc.