To test the prediction that digestive responses digestibility, intake and passage time-of generalist herbivores vary with different diets, feeding trials were conducted in Venezuela with two sympatric tortoise species, Geochelone carbonaria and G. denticulata. Three single-species diets (two fruit, one foliage) were fed to both species. For a given diet, digestibility, mass-specific intake and passage time did not differ between the two tortoise species, nor did they vary by sex or body mass within each species. However, the digestive parameters varied for tortoises feeding on the different diets. The responses ranged from nearly abandoning cell wall fermentation and depending entirely on extraction of cell contents to relying heavily on cell wall fermentation. Therefore, these generalist herbivores have flexible digestive responses that are influenced by diet, not fixed digestive responses that limit the diet, as previously observed in other generalist herbivores. A three-part classification of herbivores (specialist, specialized mixed feeder and opportunistic mixed feeder) is suggested as an approach to understanding flexible and inflexible digestive strategies in herbivores.