  Auxiliary field methods in D=2 (or 3), N=2 supersymmetric (SUSY) nonlinear
sigma models (NLSMs) are studied. For these models auxiliary fields as Lagrange
multipliers belong to a vector or a chiral superfield, which gives a Kahler
quotient of complexified gauge group or a holomorphic constraint on it,
respectively. Using these, NLSMs on all Hermitian symmetric spaces were
formulated previously. In this paper, we formulate new SUSY NLSMs on some
rank-two Kahler coset spaces as SUSY gauge theories with two Fayet-Iliopoulos
parameters.
