  We show that the interplay between the LHC and the e^+ e^- International
Linear Collider (ILC) with sqrt{s}=500 GeV might be crucial for the
discrimination between the minimal and next-to-minimal supersymmetric standard
model. We present an NMSSM scenario that cannot be distinguished from the MSSM
by cross sections and mass measurements if only the light neutralinos and the
lightest chargino are kinematically accessible, even if one of the neutralinos
has a significant singlino component. Mass predictions for the heavier
neutralinos from the ILC analysis and their observation at the LHC lead to an
identification of the neutralino mixing character and the underlying
supersymmetric model in a combined LHC/ILC analysis. In our numerical example
we include errors in the mass measurements and use standard methods of
supersymmetric parameter determination.
