Industry is dominated by dynamic systems such as process control of chemical plants or steel plants and power generation, ranging to areas such as ecological systems and traffic systems. A challenging problem is to perform real-time monitoring and diagnosis of such dynamic systems. The paper describes the work of the TIGER ESPRIT Project in performing real-time situation assessment of dynamic systems. The goal of TIGER is to monitor a complex dynamic system in real time and make an assessment of whether it is working properly. If it is not working properly, it is desirable to identify the cause of the problem either from a set of known faults or to characterise an unknown fault. This work is applied in the application domain of condition monitoring of gas turbines. The project is developing and demonstrating its techniques on two industrial gas turbines; a 28 mW gas turbine used as the prime power for a chemical plant and a small auxiliary power gas turbine used in aviation. The Project is investigating a variety of tools and techniques for real-time situation assessment. These include a high-speed rule-based compiler, a situation assessment tool able to monitor dynamic responses over time, qualitative and numerical prediction of turbine response, and model-based diagnosis to help identify unknown faults. A prototype system is currently in use at a chemical plant performing monitoring and diagnosis in real-time.