Elucidating SUSY in the Interplay of LHC and ILC - $\bar \tau$co-annihilation models

While the current 7/8 TeV results form the LHC excludes highly constrainedSUSY models with a light sparticle spectrum, less constrained modelsare still viable. Certain such models promise both discovery ofcoloured sparticles during the upcomming 14 TeV run of the LHC, and a richspectrum of non-coloured states, accessible at the ILC. LHC might ormight not give a hint to the existence of these electro-weak states, butonly at the ILC can measurements with sufficient precision be done toelucidate the details of the model. This contribution discusses howthe combined observations from LHC and ILC can be used to determine MSSMparameters in models with large numbers of free parameters.We illustrate the possible interplay between measurements at ILC and LHC by aconcrete example, compatible with all current constraints. It is a full SUSY modelwhich features a small stau-LSP mass difference, and quite heavy coloured particles.The model has been studied using detailed detector simulation of both LHC and ILCdetectors