In tiny metallic nanostructures, quantum confinement and nonlocal response change the collective plasmonic behaviour with resulting important consequences for e.g. field-enhancement and extinction cross sections. Here we report on nonlocal resonances in the hydrodynamical Drude model for plasmonic nanostructures that have no counterpart in the local-response Drude model. Even though there are no additional resonances in the visible due to nonlocal response, plasmonic field enhancements are affected by nonlocal response. We present both analytical results for simple geometries and our numerical implementation for arbitrary geometries, and address computational issues related to the several length scales involved.