Past model studies have projected a global decrease in marine net primary production (NPP) over the 21st century, but these studies focused on the multi-model mean rather than on the large inter-model differences. Here, we analyze model-simulated changes in NPP for the 21st century under IPCC's high-emission scenario RCP8.5. We use a suite of nine coupled carbon-climate Earth system models with embedded marine ecosystem models and focus on the spread between the different models and the underlying reasons. Globally, NPP decreases in five out of the nine models over the course of the 21st century, while three show no significant trend and one even simulates an increase. The largest model spread occurs in the low latitudes (between 30 degrees S and 30 degrees N), with individual models simulating relative changes between -25 and +40 %. Of the seven models diagnosing a net decrease in NPP in the low latitudes, only three simulate this to be a consequence of the classical interpretation, i.e., a stronger nutrient limitation due to increased stratification leading to reduced phytoplankton growth. In the other four, warming-induced increases in phytoplankton growth outbalance the stronger nutrient limitation. However, temperature-driven increases in grazing and other loss processes cause a net decrease in phytoplankton biomass and reduce NPP despite higher growth rates. One model projects a strong increase in NPP in the low latitudes, caused by an intensification of the microbial loop, while NPP in the remaining model changes by less than 0.5 %. While models consistently project increases NPP in the Southern Ocean, the regional inter-model range is also very substantial. In most models, this increase in NPP is driven by temperature, but it is also modulated by changes in light, macronutrients and iron as well as grazing. Overall, current projections of future changes in global marine NPP are subject to large uncertainties and necessitate a dedicated and sustained effort to improve the models and the concepts and data that guide their development.