  The HEGRA system of four Imaging Atmospheric Cherenkov Telescopes (IACTs) has
been used to extensively observe extragalactic objects. In this paper we
describe the search for TeV emission from nine very promising potential TeV
sources, namely eight ``high frequency'' BL Lac objects (HBLs), and the object
``BL Lacertae'' itself. These objects were observed during 1997 and 1998
seasons, with total integration times ranging between one and fifteen hours.
  No evidence for emission was found from any of these objects and the upper
limits on the integral energy flux above ~750 GeV are on the level of a few
times 10^-12 erg cm^-2 s^-1. For the two objects BL Lacertae and 1ES 2344+51.4,
we discuss the astrophysical implications of the TeV flux upper limit, using
also information from the X-ray and gamma-ray bands as measured with the All
Sky Monitor (ASM) of RXTE (1.3-12.0 keV) and with EGRET (30 MeV - 20 GeV).
