We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled temporal algebra defineslabeled disjunctive metric pointbased constraints, where each disjunct in each input disjunctive constraint is univocally associated to a label. Reasoning algorithms manage labeled constraints, associated label lists, and sets of mutually inconsistent disjuncts. These algorithms guarantee consistency and obtain a minimal network. Additionally, constraints can be organized in a hierarchy of alternative temporal contexts. Therefore, we can reason on context-dependent disjunctive metric constraints on intervals and points. Moreover, the model is able to represent non-binary constraints, such that logical dependencies on disjuncts in constraints can be handled. The computational cost of reasoning algorithms is exponential in accordance ...