South Africa's only nuclear power station is situated at Koeberg on the west coast, about 30 km north of Cape Town. Wind direction, wind speed, rainfall and other meteorological data are collected continuously by the Koeberg weather station with a view to their use in radioactive plume modelling, inter alia. The wind direction data consist of hourly values of average wind direction over the preceding hour at 35 m above ground level. The period covered is 1 May 1985 to 30 April 1989 inclusive. The chapter discusses the Koeberg wind direction data, with a view to demonstrating some variations of hidden Markov models that could be applied to data such as these. Although it illustrates the fitting of models to categorical series, it ignores the fact that the observations of direction are available in degrees, and it ignores the circular nature of the observations.