The authors give a kneading theory for the class of continuous maps of the circle of degree with a single maximum and a single minimum. For a map of this class they characterise the set of itineraries depending on the rotation interval. From this result they obtain lower and upper bounds of the topological entropy and of the number of periodic orbits of each period. These lower bounds appear to be valid for a general continuous map of the circle of degree one. © 1990 IOP Publishing Ltd.