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We show that scalar as well as vector and tensor metric perturbations in the Randall-Sundrum II braneworld allow normalizable tachyonic modes, i.e., possible instabilities. These instabilities require nonvanishing initial anisotropic stresses on the brane. We show with a specific example that within the Randall-Sundrum II model, even though the tachyonic modes are excited, no instability develops. We argue, however, that in the cosmological context instabilities might in principle be present. We conjecture that the tachyonic modes are due to the singularity of the orbifold construction. We illustrate this with a simple but explicit toy model.