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This thesis considers nonparametric predictive inference for lifetime data that include right-censored observations. The assumption A((_m)) proposed by Hill in 1968 provides a partially specified predictive distribution for a future observation given past observations. But it does not allow right-censored data among the observations. Although Berliner and Hill in 1988 presented a related nonparametric method for dealing with right-censored data based on A((_n)), they replaced 'exact censoring information' (ECI) by 'partial censoring information' (PCI), enabling inference on the basis of A((_n)). We address if ECI can be used via a generalization of A((_n)).We solve this problem by presenting a new assumption 'right-censoring A((_n))' (rc- A((_n)), which generalizes A((_n)). The assumption rc- A((_n)) presents a partially specified predictive distribution for a future observation, given the past observations including right-censored data, and allows the use of ECI. Based on rc-A((_n)), we derive nonparametric predictive inferences (NPI) for a future observation, which can also be applied to a variety of predictive problems formulated in terms of the future observation. As applications of NPI, we discuss grouped data and comparison of two groups of lifetime data, which are problems occurring frequently in reliability and survival analysis.