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Pair-production of the superpartner of the $τ$-lepton, the $\tildeτ$, is one of the most interesting channels to search for SUSY in: The $\tildeτ$ is likely to be the lightest scalar lepton, and the signature of $\tildeτ$ pair production is one of the experimentally most difficult ones, thereby constituting the "worst" possible scenario for SUSY searches. The current model-independent $\tildeτ$ limits comes from analyses performed at LEP but they suffer from the limited energy of this facility. Limits obtained at the LHC do extend to higher masses, but they are only valid under strong assumptions. The International Linear Collider, the ILC, is a future electron-positron collider, to operate initially at an energy of 250 GeV, then to be upgraded to 500 GeV, and possibly to 1 TeV at a later stage. ILC will be a powerful facility for SUSY searches. The capability of the ILC for determining exclusion/discovery limits for the $\tildeτ$ in a model-independent way is shown in this paper. A detailed study of the "worst" scenario for $\tildeτ$ exclusion/discovery, taking into account the effect of the $\tildeτ$ mixing on $\tildeτ$ production cross-section and detection efficiency, is presented. The study also includes an analysis of the effect of the overlay particles in the $\tildeτ$ searches. The conclusion is that both the exclusion and discovery reaches for this "worst" case would extend to only a few GeV below the kinematic limit at the ILC. Also scenarios with the $\tildeτ$ and the Lightest SUSY Particle (the LSP) quite close in mass can be discovered or excluded at most $\tildeτ$ masses. The studies were done using detailed detector simulation of the ILD concept at the ILC. For signal, the fast detector simulation SGV was used, while the full Geant4 based DDSim was used for the standard model backgrounds.