  We study the nonlocal response of a confined electron gas within the
hydrodynamical Drude model. We address the question whether plasmonic
nanostructures exhibit nonlocal resonances that have no counterpart in the
local-response Drude model. Avoiding the usual quasi-static approximation, we
find that such resonances do indeed occur, but only above the plasma frequency.
Thus the recently found nonlocal resonances at optical frequencies for very
small structures, obtained within quasi-static approximation, are unphysical.
As a specific example we consider nanosized metallic cylinders, for which
extinction cross sections and field distributions can be calculated
analytically.
