Approximately 20% of patients diagnosed with a phaeochromocytoma or paraganglioma carry a germline mutation in one of the succinate dehydrogenase (SDHx) genes (SDHA, SDHB, SDHC and SDHD), which encode the four subunits of the SDH enzyme. When a pathogenic SDHx mutation is identified in an affected patient, genetic counselling is proposed for first-degree relatives. Optimal initial evaluation and follow-up of people who are asymptomatic but might carry SDHx mutations have not yet been agreed. Thus, we established an international consensus algorithm of clinical, biochemical and imaging screening at diagnosis and during surveillance for both adults and children. An international panel of 29 experts from 12 countries was assembled, and the Delphi method was used to reach a consensus on 41 statements. This Consensus Statement covers a range of topics, including age of first genetic testing, appropriate biochemical and imaging tests for initial tumour screening and follow-up, screening for rare SDHx-related tumours and management of elderly people who have an SDHx mutation. This Consensus Statement focuses on the management of asymptomatic SDHx mutation carriers and provides clinicians with much-needed guidance. The standardization of practice will enable prospective studies in the near future.