  We study renormalizable nonlinear sigma-models in two dimensions with N=2
supersymmetry described in superspace in terms of chiral and complex linear
superfields. The geometrical structure of the underlying manifold is
investigated and the one-loop divergent contribution to the effective action is
computed. The condition of vanishing beta-function allows to identify a class
of models which satisfy this requirement and possess N=4 supersymmetry.
