This paper analyses two well-known features of interest rates, namely their time dependence and their cyclical structure. Specifically, it focuses on the monthly Euribor rate, using monthly data from January 1994 to May 2011. Models based on fractional integration at the long run or zero frequency, although adequately describing the persistent behaviour of the series, do not take into account its cyclical structure. Therefore, a more general cyclical fractional model is considered. Future directions for research in this context are also discussed.