Background: Intrinsic capacity (IC) is a comprehensive measure of physical and mental capacities central to the World Health Organization healthy ageing framework. Studies from England and China suggest that more recently born cohorts enter older age with higher IC and experience slower declines, but it is unknown whether similar improvements are occurring in other settings, among adults under 60 years, and across socioeconomic groups. Methods: We analysed seven waves of the Survey of Health, Ageing and Retirement in Europe from 2004 to 2022, including 80,105 adults aged 50 years or older in ten countries. IC was derived using confirmatory factor analysis with five subdomains: cognitive, psychological, sensory, locomotor, and vitality. Multilevel growth-curve models estimated associations of birth year with IC at first interview and with within-person change over follow-up, and examined variation by country, sex, and socioeconomic status. Findings: More recently born participants had higher IC intercepts (coefficient 0.797, 95% CI 0.780 to 0.815) and slower rates of decline (coefficient 0.426, 95% CI 0.372 to 0.480). Similar trends were observed for subdomains, but improvements in both IC and its subdomains were smaller among the most recently born participants. Countries with lower IC levels in the 1920 birth cohort showed larger gains in initial IC across cohorts, but smaller improvements in rates of decline. Sex differences narrowed. Gains were significantly smaller in the lowest socioeconomic group. Interpretation: Across diverse European settings, older adults are experiencing better health and slower functional decline than previous generations. However, these positive trends are unequally distributed and may be reaching a ceiling in more developed settings.