1. The functional response, i.e. the quantity of food consumed per unit of time as a function of food availability, is a central process in foraging ecology. The application of this concept to foraging by mammalian herbivores has led to major insights into the process of resource acquisition, but it has so far been little used to understand foraging in avian herbivores. 2. In this study, we describe the functional responses of three grazing Anatidae, the wigeon Anas penelope L. (mean body mass in this study 620 g), the barnacle goose Branta leucopsis B. (2000 g), and the greylag goose Anser anser L. (3500 g). We measured instantaneous intake rates on eight grass heights from 1 cm to 12 cm, as well as pecking rates and peck sizes, and used the Spalinger–Hobbs model developed for mammalian herbivores to explore the mechanisms limiting intake in these three species. 3. Greylag geese increased their intake rate with increasing food availability (a Type II response), wigeon showed a weak quadratic (Type IV) response, and intake rate by barnacle geese did not vary significantly across the range of variability we offered the birds. 4. Intake rates differed markedly between individuals, especially in greylag geese, where body mass explained much of the variation. For individuals in all three species, peck sizes strongly influenced instantaneous intake rates, and the size of the bill (width in particular) appeared to be an important determinant of peck size. 5. Peck sizes increased with sward height (although only very weakly in wigeon), but so did cropping time for wigeon and barnacle geese, which led to a significant decline of intake rates on the tallest grass, at least in the small wigeon. For these very selective small herbivores, the time to crop a mouthful was therefore a significant limiting factor for the birds' instantaneous intake rate (in addition to peck size and swallowing time). This differs markedly from the situation in mammalian herbivores where bite size (through chewing time) is the principal controlling process in food concentrated patches, a result that we found in greylag geese. We discuss the differences in foraging between the three species in relation to their principal food resources, body mass and bill morphology.