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1. The development of models of the relationship between biodiversity and ecosystem function(BEF) has advanced rapidly over the last 20 years, incorporating insights gained through extensiveexperimental work. We propose Generalised Diversity-Interactions models that include many of thefeatures of existing models and have several novel features. Generalised Diversity-Interactions modelscharacterise the contribution of two species to ecosystem function as being proportional to theproduct of their relative abundances raised to the power of a coefficient h.2. A value of h < 1 corresponds to a stronger than expected contribution of species’ pairs to ecosystemfunctioning, particularly at low relative abundance of species.3. Varying the value of h has profound consequences for community-level properties of BEF relationships,including: (i) saturation properties of the BEF relationship; (ii) the stability of ecosystemfunction across communities; (iii) the likelihood of transgressive overyielding.4. For low values of h, loss of species can have a much greater impact on ecosystem functioningthan loss of community evenness.5. Generalised Diversity-Interactions models serve to unify the modelling of BEF relationships asthey include several other current models as special cases.6. Generalised Diversity-Interactions models were applied to seven data sets and three functions:total biomass (five grassland experiments), community respiration (one bacterial experiment) andnitrate leaching (one earthworm experiment). They described all the nonrandom structure in the datain six experiments, and most of it in the seventh experiment and so fit as well or better than competingBEF models for these data. They were significantly better than Diversity-Interactions models infive experiments.7. Synthesis. We show that Generalized Diversity-Interactions models quantitatively integrate severalmethods that separately address effects of species richness, evenness and composition on ecosystemf