  We study the problem of the boundary behaviour of the Bergman kernel and the
Bergman completeness in some classes of bounded pseudoconvex domains, which
contain also non-hyperconvex domains. Among the classes for which we prove the
Bergman completeness and the convergence of the Bergman kernel to infinity
while tending to the boundary are all bounded pseudoconvex balanced domains,
all bounded Hartogs domains with balanced fibers over regular domains and some
bounded Laurent-Hartogs domains.
