Nine months' seeing statistics at the Observatorio del Roque de los Muchachos (ORM) are presented. Measurements were taken with a differential image motion monitor on top of a 5-m high tower. From the whole campaign the mean seeing is 0.76", the median value is 0.64" and 7% of the time the seeing is better than 0.3". The best seeing measured is 0.17". A seasonal variation is noticeable, better seeing conditions appearing during summer, which corresponds to the occurrence of a well-defined inversion layer due to the high prevalence of trade winds. During the summer, 50% of the time seeing is better than 0.54", value which drops to 0.46" during June, with a narrow distribution (rms = 0.17"). These figures place the ORM among, or better than, the best astronomical sites (Paranal and La Silla, Chile) where seeing statistics are available. When inspecting individual nights, it sporadically happens that seeing deteriorates abruptly and slowly recovers, with a 1.2-hour exponential decay time. This phenomenon is interpreted in terms of meteorological instabilities (gravity waves) which trigger a turbulent regime.