In this paper we discuss an approach to the analysis of mortality and longevity limits when survival data on related individuals with and without observed covariates are available. The approach combines the ideas of demography and survival analysis with methods of quantitative genetics and genetic epidemiology. It allows us to analyze the genetic structure of frailty in the Cox-type hazard model with random effects. We demonstrate the implementation of this strategy to survival data on Danish twins. We then evaluate the resulting lower bounds for biological limits of human longevity. Finally, we discuss the limitations of this approach and directions of further research.