  The cosmological evolution of free massless vector or tensor (but not gauge)
fields minimally coupled to gravity is analyzed. It is shown that there are
some unstable solutions for these fields in De Sitter background. The back
reaction of the energy-momentum tensor of such solutions to the original
cosmological constant exactly cancels the latter and the expansion regime
changes from the exponential to the power law one. In contrast to the
adjustment mechanism realized by a scalar field the gravitational coupling
constant in this model is time-independent and the resulting cosmology may
resemble the realistic one.
