Residential and service (office) buildings consume a large proportion of primary energy in Europe in the form of electricity and all other energy carriers. In response to this, the concept of near Zero Energy Buildings (nZEB) has been developed. These buildings have very low energy demands and integrate renewable energy to supply residual demand. nZEBs aim to increase energy efficiency from a demand-side user perspective. When looking at the entire energy system, there are also energy efficiency gains to be achieved on the supply-side. For example, from a district heating system. If an energy system becomes more efficient on the supply-side, then the question is how much energy needs to be saved on the demand-side, for instance by low energy buildings such as nZEBs. The purpose of this paper is to analyse and understand the implications from building new low energy buildings, i.e. nZEBs, within an energy system that is (a) transitioning to 100% renewable energy and (b) has substantially improved supply-side energy efficiency. A case study from Denmark is used to understand the outcome for the energy system when these new buildings are built in this context. The methodology and results of this study could be replicated for other European countries as well. The analysis looks at the total energy system heat savings, costs and biomass consumption. The paper shows that these new low energy buildings with very low heat demand do not deliver the expected benefits for the 100% renewable energy system transition in Denmark. This is due to the increased efficiency and flexibility of the energy supply system in the future. However, deep renovations of existing buildings are necessary. Furthermore, this paper demonstrates based on the Danish case, that as European countries decarbonise their energy systems over the next decades, they will need to carry out detailed energy system analysis to determine the extent to which heat demand should be reduced in buildings within the context of the transitioning energy system.