Despite a substantial literature on the links between social relationships and mortality, the size of the relative risks from loneliness, social isolation, and living alone, remain controversial. Further research is therefore important given demographic changes meaning that more people are living alone, for longer, and with chronic health conditions. Using 19 waves of high-quality Australian longitudinal data we provide new evidence using multiple measures of social relationships, model specifications, and adjustments for confounding. We focus on chronic measures of (poor) social relationships and provide separate estimates by gender. We find that both functional and structural aspects of social relationships are independently strongly associated with all-cause mortality. We estimate a hazard ratio for loneliness of 1.41, which is greater for males (1.55) than females (1.24). These hazard ratios are larger than found for social isolation (1.19). We also find a strong relationship between being an active member of a club and reduced mortality risk, but no evidence that living alone is an independent risk factor. We provide useful comparisons with the mortality risks associated with smoking and household income. Overall, our findings suggest that interventions should focus on reducing both loneliness and social isolation, as well as encouraging active social participation.