  We analyze superconducting state (both s and d - wave) in a simple exactly
solvable model of pseudogap state, induced by short - range order fluctuations
(e.g. antiferromagnetic), which is based upon model Fermi - surface with "hot
patches". It is shown that superconducting energy gap averaged over these
fluctuations is non zero even for the temperatures larger than mean - field T_c
of superconducting transition in a sample as a whole. For temperatures T>T_c
superconductivity apparently exists within separate regions ("drops"). We study
the spectral density and the density of states and demonstrate that
superconductivity signals itself in these already for T>T_c, while at T_c
itself nothing special happens from this point of view. These anomalies are in
qualitative agreement with a number experiments on underdoped cuprates.
