  A number of rotation-powered millisecond pulsars are powerful sources of
X-ray emission. We present predictions for the spectral characteristics of
these sources at gamma-ray energies, using a model for acceleration and pair
cascades on open magnetic field lines above the polar caps. Since these pulsars
have low surface magnetic fields, the majority do not produce sufficient pairs
to completely screen the accelerating electric field allowing particle
acceleration to high altitude. The resulting emission above 1 GeV comes from
curvature radiation by primary electrons with radiation-reaction-limited
Lorentz factors. The spectra are very hard power-laws with exponential cutoffs
between 1 and 50 GeV, and the spectral power peaks near the cutoff energy.
Millisecond pulsars are thus ideal targets for air-Cherenkov detectors that are
able to reach energy thresholds below 50 GeV.
