Cognitive abilities, particularly memory, normally decline with age. However, some individuals, often designated as superagers, can reach late life with the memory function of individuals 30 years younger. We aimed to characterise the brain structure of superagers and identify demographic, lifestyle, and clinical factors associated with this phenotype. We selected cognitively healthy participants from the Vallecas Project longitudinal cohort recruited between Oct 10, 2011, and Jan 14, 2014, aged 79·5 years or older, on the basis of their delayed verbal episodic memory score. Participants were assessed with the Free and Cued Selective Reminding Test and with three non-memory tests (the 15-item version of the Boston Naming Test, the Digit Symbol Substitution Test, and the Animal Fluency Test). Participants were classified as superagers if they scored at or above the mean values for a 50-56-year-old in the Free and Cued Selective Reminding Test and within one standard deviation of the mean or above for their age and education level in the three non-memory tests, or as typical older adults if they scored within one standard deviation of the mean for their age and education level in the Free and Cued Selective Reminding Test. Data acquired as per protocol from up to six yearly follow-ups were used for longitudinal analyses. We included 64 superagers (mean age 81·9 years; 38 [59%] women and 26 [41%] men) and 55 typical older adults (82·4 years; 35 [64%] women and 20 [36%] men). The median number of follow-up visits was 5·0 (IQR 5·0-6·0) for superagers and 5·0 (4·5-6·0) for typical older adults. Superagers exhibited higher grey matter volume cross-sectionally in the medial temporal lobe, cholinergic forebrain, and motor thalamus. Longitudinally, superagers also showed slower total grey matter atrophy, particularly within the medial temporal lobe, than did typical older adults. A machine learning classification including 89 demographic, lifestyle, and clinical predictors showed that faster movement speed (despite no group differences in exercise frequency) and better mental health were the most differentiating factors for superagers. Similar concentrations of dementia blood biomarkers in superager and typical older adult groups suggest that group differences reflect inherent superager resistance to typical age-related memory loss. Factors associated with dementia prevention are also relevant for resistance to age-related memory decline and brain atrophy, and the association between superageing and movement speed could provide potential novel insights into how to preserve memory function into the ninth decade. Queen Sofia Foundation, CIEN Foundation, Spanish Ministry of Science and Innovation, Alzheimer's Association, European Research Council, MAPFRE Foundation, Carl Zeiss Foundation, and the EU Comission for Horizon 2020. For the Spanish translation of the abstract see Supplementary Materials section.