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In order to achieve greenhouse gas neutrality, hydrogen generated from renewable sources will play an important role. Additionally, as underlined in the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC), new technologies to remove greenhouse gases from the atmosphere are required on a large scale. A novel concept for hydrogen production with net negative emissions referred to as HyBECCS (Hydrogen Bioenergy with Carbon Capture and Storage) combines these two purposes in one technological approach. The HyBECCS concept combines biohydrogen production from biomass with the capture and storage of biogenic carbon dioxide. Various technology combinations of HyBECCS processes are possible, whose ecological effects and economic viability need to be analyzed in order to provide a basis for comparison and decision-making. This paper presents fundamentals for the techno-economic and environmental evaluation of HyBECCS approaches. Transferable frameworks on system boundaries as well as emission, cost, and revenue streams are defined and specifics for the application of existing assessment methods are elaborated. In addition, peculiarities concerning the HyBECCS approach with respect to political regulatory measures and interrelationships between economics and ecology are outlined. Based on these considerations, two key performance indicators (KPIs) are established, referred to as levelized cost of carbon-negative hydrogen (LCCNH) and of negative emissions (LCNE). Both KPIs allow deciding whether a specific HyBECCS project is economically viable and allows its comparison with different hydrogen, energy provision, or negative emission technologies (NETs).