A clear and agreed definition of Zero Emission Building (ZEB) is yet to be achieved, both internationally and in Norway. However, it is understood that both the definition and the surrounding energy supply system will affect significantly the way buildings are designed to achieve the ZEB goal. Since the energy system in Europe is expected to change significantly in the coming decades, especially for electricity, it is indispensable to tie the definition of ZEB to possible scenarios on such development of the energy system. A scenario is defined as a combination of options chosen within a framework of different uncertain futures. Two uncertainties are identified as most important for the development and deployment of ZEB: Technology development and Public attitude. These two uncertainties are used to span out a set of four relevant futures, also termed storylines, as a common background for scenario analysis. A formal definition of ZEB is characterized by a set of criteria that are: the system boundary, feeing-in possibilities, balance object, balancing period, credits, crediting method, energy performance and mismatch factors. For each criterion different options are available, and the choice of which options are more appropriate to define ZEBs may depend on the storyline features.