To date, impacts of ionising radiations have been largely disregarded in Life Cycle Assessment (LCA). This omission can be linked to the lack of a standard and comprehensive framework for including the effects of radionuclides alongside other emissions from industrial processes. Drawing on a recent review of Radiological Impact Assessment methodologies for LCA studies, this article proposes an overarching framework for integrating impacts of radionuclides in the Impact Assessment phase of LCA. From this framework, two alternative methodologies have been derived. They differ mainly in the way transport and dispersion of radionuclides in the environment are modelled: UCrad represents the first-of-its-kind compartment-type methodology for radionuclides, whereas the alternative Critical Group Methodology (CGM) has been adapted from standard Risk Assessment practices. Characterisation factors for a range of emitted species have been calculated using both methodologies and compared with those obtained from the Human Health Damages methodology, which is the only approach to radiological impacts yet implemented in LCA. For both UCrad and CGM the results are in general agreement with the Human Health Damages methodology, but UCrad gives factors closer to those obtained by the CGM approach. UCrad represents a major step towards incorporating ionising radiation impacts in LCIA. A subsequent paper will explore quantitatively the main differences between the UCrad and CGM methodologies