Social isolation and loneliness have been recognized as problems older people face due to their adverse effects on health and mortality, but very few researchers have analyzed their co-occurrence, which might be particularly prevalent and critical among the very old. In this study, we investigated the prevalence of combinations of social isolation and loneliness among near-centenarians and centenarians. We used data collected from 94 individuals aged 95-107 from the Fordham Centenarian Study. We built a four-group typology and explored associations with individual characteristics in various domains (demographic, socioeconomics, social, health, care, and psychological) with multinomial logistic regression models. Considering their combinations, the most prevalent groups were "isolated and lonely" and "neither isolated nor lonely" (29.8% and 28.7%, respectively). The "lonely but not isolated" (20.2%) and "isolated but not lonely" (21.3%) groups were also notably large. The likelihood of belonging to each group varied according to various individual characteristics, such as education, health, and personality. Social isolation and loneliness are distinct phenomena among centenarians. The consideration of their varied combination can help better assess life conditions at very old ages. Taking into account the differences between groups can facilitate the design of tailored interventions to improve the lives of near-centenarians and centenarians.