  Recently some experimental evidences have been obtained in favour of the
existence of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
superconducting state in heavy-fermion superconductor CeCoIn_{5} and organic
superconductor -(BETS)_{2}FeCl_{4}. However the unambiguous identification of
FFLO state remains very difficult. We present the theoretical studies of the
Gaussian fluctuations near the tricritical point (where the FFLO modulation
appears) and demonstrate that the behavior of the fluctuational specific heat,
paraconductivity and diamagnetism is qualitatively different from the usual
superconducting transition. Special values of the critical exponent and the
crossovers between different fluctuational regimes may provide a unique test
for the FFLO state appearance.
