The HEGRA system of four Imaging Atmospheric Cherenkov Telescopes (IACTs) h
as been used to extensively observe extragalactic objects. In this paper we
describe the search for TeV emission from nine very promising potential Te
V sources, namely eight "high frequency" BL Lac objects (HBLs), and the obj
ect "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 uppe
r limits on the integral energy flux above similar to 750 GeV are on the le
vel of a few times 10(-12) erg cm(-2) s(-1). For the two objects BL Lacerta
e and IES 2344+51.4, we discuss the astrophysical implications of the TeV f
lux 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).