The order-of-arrival (OOA) of a stream of objects moving along a direction is important for decision making in logistic and industrial applications. As an example, the dispatch of luggage in airports requires to determine their OOA at check- points; as another example, the automatic steering of items in supply chains requires to sort and identify them while moving on a conveyor belt. This paper establishes a general framework for determining the OOA of objects that are moving along a monitored direction via radio-frequency identification (RFID) systems. Three techniques for OOA tracking are proposed and developed for objects equipped with RFID tags possessing ranging capabilities. The benefits of the proposed techniques are validated experimentally based on measurements gathered with an RFID system operating in an indoor environment.