Consider a stream of status updates generated by a source, where each update is of one of two types: priority or ordinary; these updates are to be transmitted through a network to a monitor. We analyze a transmission policy that treats updates depending on their content: ordinary updates are served in a first-come first-served fashion, whereas the priority updates receive preferential treatment. An arriving priority update discards and replaces any currently-in-service priority update, and preempts (with eventual resume) any ordinary update. We model the arrival processes of the two kinds of updates as independent Poisson processes and the service times as two (possibly different rate) exponentials. We find the arrival and service rates under which the system is stable and give closed-form expressions for average peak age and a lower bound on the average age of the ordinary stream. We give numerical results on the average age of both streams and observe the effect of each stream on the age of the other.