This paper proposes real-time traffic management algorithms over a multihop optical network. Our algorithms consider dynamic scheduling of (time, wavelength) slots in a multihop TWDM transmission schedule, so that a set of time-critical messages can meet their hard (and, soft) deadlines. Hard real-time messages are assigned to the highest priority level, while soft real-time messages are assigned to user-defined, progressively lower priority levels. The objective is to schedule these messages, all or as many as possible following the priority ordering. Previous research in this direction are either static scheduling policies (which cannot adapt to varying traffic conditions), or dynamic scheduling but for non-realtime traffic. Performance is measured in simulation. Where input factors include load, proximity of the deadline values, relative mix of hard and soft real-time messages, and priority levels of the messages.