We study the SU(2] WZNW model over a family of elliptic curves. Starting from the formulation developed in , we derive a system of differential equations which contains the Knizhmk-Zamolodchikov-Bernard equations . Our system completely determines the N-point functions and is regarded as a natural elliptic analogue of the system obtained in  for the projective line. We also calculate the system for the 1-point functions explicitly. This gives a generalization of the results in  for si (2, C)-characters.