We investigate the off-shell N = 2 and N = 4 structure of the supersymmetric Wess-Zumino-Witten model. We present an offshell formulation of the SU (2) (x) U (1) supersymmetric WZW model in terms of N = 2 chiral and twisted chiral multiplets. We show that such a formulation is not possible for any other group and suggest a larger multiplet structure to cover these cases.