  The theoretical investigation of spectral functions and pseudogap in systems
with strongly correlated electrons is discussed, with the emphasis on the
single-band t-J model as relevant for superconducting cuprates. The evidence
for the pseudogap features from numerical studies of the model is presented.
One of the promising methods to study spectral functions is the method of
equations of motion. The latter can deal systematically with the local
constraints and projected fermion operators inherent for strongly correlated
electrons. In the evaluation of the self energy the decoupling of spin and
single-particle fluctuations is performed. In an undoped antiferromagnet the
method reproduces the selfconsistent Born approximation (SCBA). For finite
doping the approximation evolves into a paramagnon contribution which retains
large incoherent contribution in the hole part. On the other hand, the
contribution of longer-range spin fluctuations is essential for the emergence
of the pseudogap. The latter shows up at low doping in the effective truncation
of the large Fermi surface, reduced electron density of states and at the same
time reduced quasiparticle density of states at the Fermi level.
