Two trials were conducted, in France (t1) and Tunisia (t2). T1 (a replicated Latin square design, 6 wethers) with natural grassland hay at 3 intake levels. T2 (4 dry ewes) receiving a vetch and oat hay for 10 weeks at different levels, too. Five periods of measurements were reported. In t1, neutral detergent fibre (NDF) digestibility was higher at 20 than at 60 and 100 percent of maintenance requirements. The same trend was observed for NDF retention time in the rumen whereas in situ degradability and activity of fibrolytic enzymes were not modified by intake. In t2, underfeeding resulted in a large decrease in NDF digestibility, despite a very long retention time of particles in the rumen. It was not explained by variations in in situ degradability, which was not sensitive enough to indicate differences in microbial activity. These trials show potential differences in response to a same decrease in intake. The causes of the drop in digestibility at low intake in t2 remain to be explained.