The orbital autocorrelation functions of two possible isotropic Fermi superfluids, of the BCS and the BW type, are examined from the point of view of inequalities resulting from thermodynamic stability of liquids. The negative sign of static functions, as well as the sign of their residues are investigated. Moreover, the analogues of Leggett's inequality for spin autocorrelation functions of BW liquids are considered. For orbital functions, the application of their generalized formal solutions, introduced previously by the author, are the source of obtained results. In all cases, in which a complete estimate of the autocorrelation functions is possible, the constraints imposed on Landau parameters for superfluids systems are not stronger than the analogous ones for normal systems, which is in agreement with common belief.
