In many areas repeated observations of processes are made in order to detect changes. Typical examples are industrial process control, public health monitoring and financial trading systems. These processes contain random components, so statistical methodology is needed in order to separate the important changes from the stochastic variation. This project focuses on cyclical processes such as business cycles or hormone cycles, where the aim is to detect the turning points to make business-cycle forecasts or for natural family planning. The overall goal of the project is to construct and evaluate systems for quick and safe turning-point detection. A robust approach is used, which makes it possible to detect a turning point even if its characteristics are very different from previous turns. The quality of a system depends on both the construction of the system and the characteristics of the monitored process. We plan studies of robustness regarding mis-specifications. In the analysis of business cycles or hormone cycles several indicators are often studied. Surveillance systems that combine information from different processes are planned.