New epigenomics technologies are being developed and used for the detection and prediction of various types of cancer. By allowing for timely intervention or preventive measures, epigenomics technologies show promise for public health, notably in population screening. In order to assess whether implementation of epigenomics technologies in population screening may be morally acceptable, it is important to understand – in an early stage of development – ethical and societal issues that may arise. We held 3 focus groups with experts in science and technology studies (STS) (n = 13) in the Netherlands, on 3 potential future applications of epigenomic technologies in screening programmes of increasing scope: cervical cancer, female cancers and ‘global’ cancer. On the basis of these discussions, this paper identifies ethical issues pertinent to epigenomics-based population screening, such as risk communication, trust and public acceptance; personal responsibility, stigmatisation and societal pressure, and data protection and data governance. It also points out how features of epigenomics (eg, modifiability) and changing concepts (eg, of cancer) may challenge the existing evaluative framework for screening programmes. This paper aims to anticipate and prepare for future ethical challenges when epigenomics technologies can be tested and introduced in public health settings.