This paper is to discuss TBM tunnelling in difficult ground conditions, when problems are met which may reduce dramatically the average progress rates and practical consequences may be such as to pose seri- ous questions on the use of mechanised TBM tunnelling versus drill and blast and other so-called traditional excavation methods. Following a few remarks on rock TBM tunnelling in relation to the selection and di- mensioning of the machine, the attention is posed on the limiting geological conditions which may be envis- aged with respect to the use of TBM tunnelling and on the importance of geological and geotechnical inves- tigations, in order to derive an appropriate understanding of the rock mass conditions along the line of the tunnel. The discussion is centered upon the relatively more important or difficult ground conditions including borability limits, instability of excavation walls, instability of excavation face, fault zones and squeezing. Whenever available to the authors and based on project experience, the point of view is illustrated by case examples, which give the opportunity to underline specific difficulties encountered and recommendations.