The non-detection of pulsed sub-TeV \gamma -rays from EGRET pulsars proves that the EGRET pulsed spectra of all \gamma -ray pulsars should terminate at energies below a few hundred GeV .
The spectrum of a typical integrated pulse profile predicted by the polar cap model resemble typically a hard component , followed by a super exponential cutoff between 1 MeV ( PSR B1509-58 ) and tens of GeV ( e.g .
Crab , PSR B1951+32 etc ) .
Outergap models predict a hard low flux component extending to TeV energies , and the stereoscopic property of the H.E.S.S .
( High Energy Stereoscopic System ) ground-based detector ( under construction ) would have the advantage to discriminate against the background above 50-100 GeV , so that such a second component may be detectable .
However , the challenge posed for any ground-based \gamma -ray detection is to prove that the instrument can detect a pure polar cap origin , whereas an outergap mechanism would provide little challenge given the rapid increase in the effective area A ( E ) with increasing energy E for Cerenkov telescopes .

Using a topological trigger in the non-imaging mode , we show that H.E.S.S .
should be able to detect pulsed emission from PSR B1706-44 within a few hours if the cutoff energy is above 30 GeV as suggested by EGRET observations .
The recently detected radio pulsar PSR J1837-0604 ( pulsar period : 96 ms ) associated with the unidentified EGRET source GeV J1837-06010 should also be detectable within a few hours if the source is pulsed and if its cutoff is similar to that of PSR B1706-44 .
H.E.S.S .
should even be able to image middle-aged , low-multiplicity pulsars for which the mean photon energy is expected to be well above 10 GeV .
Such observations should provide important constraints on the final evolutionary status of \gamma -ray pulsars and millisecond pulsars in general .