Genetic variability, kin structure and demography of a population are mutually dependent. Population genetic theory predicts that under demographically stable conditions, neutral genetic variability reaches equilibrium between gene flow and drift. However, density fluctuations and non-random mating, resulting e.g. from kin clustering, may lead to changes in genetic composition over time. Theoretical models also predict that changes in kin structure may affect aggression level and recruitment, leading to density fluctuations. These predictions have been rarely tested in natural populations. The aim of this study was to analyse changes in genetic variability and kin structure in a local population of the root vole (Microtus oeconomus) that underwent a fourfold change in mean density over a 6-year period. Intensive live-trapping resulted in sampling 88% of individuals present in the study area, as estimated from mark–recapture data. Based on 642 individual genotypes at 20 microsatellite loci, we compared genetic variability and kin structure of this population between consecutive years. We found that immigration was negatively correlated with density, while the number of kin groups was positively correlated with density. This is consistent with theoretical predictions that changes in kin structure play an important role in population fluctuations. Despite the changes in density and kin structure, there was no genetic differentiation between years. Population-level genetic diversity measures did not significantly vary in time and remained relatively high (HE range: 0.72–0.78). These results show that a population that undergoes significant demographic and social changes may maintain high genetic variability and stable genetic composition.