Creep experiments on fine-grained ice reveal the existence of three creep regimes: (1) a dislocation creep regime, (2) a superplastic flow regime in which grain boundary sliding is an important deformation process, and (3) a basal slip creep regime in which the strain rate is limited by basal slip. Dislocation creep in ice is likely climb-limited, is characterized by a stress exponent of 4.0, and is independent of grain size. Superplastic flow is characterized by a stress exponent of 1.8 and depends inversely on grain size to the 1.4 power. Basal slip limited creep is characterized by a stress exponent of 2.4 and is independent of grain size. A fourth creep mechanism, diffusional flow, which usually occurs at very low stresses, is inaccessible at practical laboratory strain rates even for our finest grain sizes of ~3 μm. A constitutive equation based on these experimental results that includes flow laws for these four creep mechanisms is described. This equation is in excellent agreement with published laboratory creep data for coarse-grained samples at high temperatures. Superplastic flow of ice is the rate-limiting creep mechanism over a wide range of temperatures and grain sizes at stresses ≲ 0.1 MPa, conditions which overlap those occurring in glaciers, ice sheets, and icy planetary interiors. ¿ 2001 American Geophysical Union