  Properties of superfluid states of two-dimensional electron systems with
critical antiferromagnetic fluctuations are investigated. These correlations
are found to result in the emergence of rapidly varying in the momentum space
terms in all components of the mass operator, including the gap function
$\Delta({\bf p})$. It is shown that a domain, where these terms reside, shrinks
with the temperature, leading to a significant difference between the
temperature $T_c$, at which superconductivity is terminated, and the
temperature $T^*$, where the gap in the single-particle spectrum vanishes.
