  We report on the search for very-high-energy gamma-ray emission from the
regions around three nearby supersonic pulsars (PSR B0355+54, PSR J0357+3205
and PSR J1740+1000) that exhibit long X-ray tails. To date there is no clear
detection of TeV emission from any pulsar tail that is prominent in X-ray or
radio. We provide upper limits on the TeV flux, and luminosity, and also
compare these limits with other pulsar wind nebulae detected in X-rays and the
tail emission model predictions. We find that at least one of the three tails
is likely to be detected in observations that are a factor of 2-3 more
sensitive. The analysis presented here also has implications for deriving the
properties of pulsar tails, for those pulsars whose tails could be detected in
TeV.
