  A sample of selected active galactic nuclei (AGN) was observed in 2003 and
2004 with the High Energy Stereoscopic System (H.E.S.S.), an array of imaging
atmospheric-Cherenkov telescopes in Namibia. The redshifts of these candidate
very-high-energy (VHE, >100 GeV) gamma-ray emitters range from z=0.00183 to
z=0.333. Significant detections were already reported for some of these
objects, such as PKS 2155-304 and Markarian 421. Marginal evidence (3.1 sigma)
for a signal is found from large-zenith-angle observations of Markarian 501,
corresponding to an integral flux of I(>1.65 TeV) = (1.5 +/- 0.6 (stat) +/- 0.3
(syst)) x 10^{-12} cm^{-2} s^{-1} or ~15% of the Crab Nebula flux. Integral
flux upper limits for 19 other AGN, based on exposures of ~1 to ~8 hrs live
time, and with average energy thresholds between 160 GeV and 610 GeV, range
from 0.4% to 5.1% of the Crab Nebula flux. All the upper limits are the most
constraining ever reported for these objects.
