The adoption of an Ecosystem Approach to environmental management requires an understanding of the complex linkages between natural capital stocks and the flows of ecosystem services from those stocks. Stock-flow relationships and dynamics have been central to much of ecosystem research, and ecologists therefore have much to contribute to the development of an ecosystem service science. Here, we explore the potential of systems analysis and systems ecology for advancing this field, particularly via holistic approaches grounded in thermodynamics and cybernetics. We contrast these with more reductionist experiment-based approaches that seek to link biodiversity to ecosystem functioning and services. Both approaches can provide valuable insights into the relationships between stocks and flows and the mechanisms behind them. The importance of scale in designing research programmes around these two approaches is discussed, particularly in the context of providing practical advice to those involved in environmental management. However, for ecosystem-science evidence to be recognised and incorporated into decision making, mainstream ecologists must be prepared to work alongside other non-science disciplines. The challenges and benefits of interdisciplinary working are reviewed, and a model framework is provided to facilitate work on socio-ecological systems.