We point out that the pseudogap phenomena observed in under-doped high-T-c,
cuprates are naturally understood as a precursor of the strong coupling su
perconductivity and this idea does not contradict with their magnetic field
dependences. The strong coupling superconductivity necessarily leads to th
e strong fluctuations with a character of the pre-formed pairs. The pre-for
med pairs have small dispersion and are thermally excited in the vicinity o
f the critical point. The gap structures of the spectral weight and the den
sity of states result from such strong fluctuations and give rise to the re
duction of the NMR spin-lattice relaxation rate in the wide temperature reg
ion. On the basis of this idea, the magnetic field dependence of the pseudo
gap phenomena is naturally shown to be remarkably small in the strong coupl
ing case. These features well explain the experiments. (C) 2000 Elsevier Sc
ience B.V. All rights reserved.