  Two-loop renormalization-group analysis for a two-dimensional electron system
with a partially flat Fermi surface has been carried out. We found that, {\it
irrespective of pairing mechanism}, the quasiparticle weight is anisotropically
suppressed due to logarithmically singular processes in the flat regions of the
Fermi surface. When the energy scale decreases, the quasiparticle weight is the
most strongly suppressed around the center of the flat region, which
qualitatively agrees with the anisotropic pseudogap behavior suggested through
the angle-resolved photoemission spectroscopy experiments for underdoped
Bi$_2$Sr$_2$CaCu$_2$O$_8$.
