The influence of Fermi liquid Landau-type interactions on the critical behaviour of superconductors and superfluids in the presence of DC magnetic fields and superflows is studied. Paramagnetic and diamagnetic instability phenomena are described in detail for singlet sand triplet p-paired superconducting Fermi liquids. The impact of Landau interactions on both instability effects is found to be significant. Inhomogeneous Larkin-Ovchinnikov superfluid states are also considered in the case of strongly interacting systems. The influence of Landau interactions on critical depairing superflows for s- and p-paired superfluids is determined. Applications of the results obtained to the description of superconductors, superfluid 3 He and 3 He- 4 He mixtures as well as the rare earth ternary compound ErRh 4 B 4 are discussed.