1. Understanding how vital rates and reproductive value change with age is fundamental to demography, life history evolution and population genetics. The universality of organism senescence has been questioned on both theoretical and empirical grounds, and the prevalence and strength of senescence remain a controversial issue. Plants are particularly interesting for studies of senescence since individuals of many species have been reported to reach very high ages. 2. In this study, we examined whether the herb Borderea pyrenaica, known to reach ages of more than 300 years, experiences senescence. We collected detailed demographic information from male and female individuals in two populations over 5 years. An unusual morphological feature in this species enabled us to obtain exact age estimates for each of the individuals at the end of the demographic study. 3. We used restricted cubic regression splines and generalized linear models to determine nonlinear effects of age and size on vital rates. We then incorporated the effects of age and size in integral projection models of demography for determining the relationship between age and reproductive value. As the species is dioecious, we performed analyses separately for males and females and examined also the hypothesis that a larger reproductive effort in females comes at a senescence cost. 4. We found no evidence for senescence. Recorded individuals reached 260 years, but growth and fecundity of female and male individuals did not decrease at high ages, and survival and reproductive value increased with age. The results were qualitatively similar also when accounting for size and among-individual vital rate heterogeneity, with the exception that male flowering probability decreased with age when accounting for size increases. 5. Synthesis. Overall, our results show that performance of both male and female plants of B. pyrenaica may increase rather than decrease at ages up to several centuries, and they support the notion that senescence may be negligible in long-lived modular organisms. This highlights the need to explore mechanisms that enable some species to maintain high reproductive values also at very high ages and to identify the evolutionary reasons why some organisms appear to experience no or negligible senescence.