We discuss a novel approach for constructing deterministic reactive systems that evolves around a temporal model which incorporates a multiplicity of timelines. This model is central to LINGUA FRANCA (LF), a polyglot coordination language and compiler toolchain we are developing for the definition and composition of concurrent components called Reactors, which are objects that react to and emit discrete events. What sets LF apart from other languages that treat time as a first-class citizen is that it confronts the issue that in any reactive system there are at least two distinct timelines involved; a logical one and a physical one-and possibly multiple of each kind. LF provides a mechanism for relating events across timelines, and guarantees deterministic program behavior under quantifiable assumptions.