  Pseudogap phenomena of high-T_c cuprates are examined. In terms of AFM
(antiferromagnetic) and dSC (d_{x^2-y^2}-wave superconducting) auxiliary fields
introduced to integrate out the fermions, the effective action for 2D electron
systems with AFM and dSC fluctuations is considered. By the self-consistent
renormalization (SCR), the NMR relaxation rate T_1^{-1}, the spin correlation
length \xi_\sigma and the pairing correlation length \xi_d are calculated. From
this calculation, a mechanism of the pseudogap formation emerges as the region
of dominant d-wave short-range order (SRO) over AFM-SRO. When damping for the
AFM fluctuation strongly depends on the dSC correlation length through the
formation of precursor singlets around (\pi,0) and (0,\pi) points in the
momentum space, the pseudogap appears in a region of the normal state
characterized by decreasing 1/T_1T and increasing AFM correlation length with
decrease in temperature. This reproduces a characteristic feature of the
pseudogap phenomena in many underdoped cuprates. When the damping becomes
insensitive to the dSC correlation length, the pseudogap region shrinks as in
the overdoped cuprates.
