  We consider the generic nonanticommutative model of chiral-antichiral
superfields on ${\cal N}={1\over 2}$ superspace. The model is formulated in
terms of an arbitrary K\"ahlerian potential, chiral and antichiral
superpotentials and can include the nonanticommutative supersymmetric
sigma-model as a partial case. We study a component structure of the model and
derive the component Lagrangian in an explicit form with all auxiliary fields
contributions. We show that the infinite series in the classical action for
generic nonanticommutative model of chiral-antichiral superfields in D=4
dimensions can be resumed in a compact expression which can be written as a
deformation of standard Zumino's lagrangian and chiral superpotential. Problem
of eliminating the auxiliary fields in the generic model is discussed and the
first perturbative correction to the effective scalar potential is obtained.
