Several systems described by the two-fluid model are considered. (1) For the superfluid 4He and 3He-4He mixtures, a new integral of motion is found, finite-temperature conditions for thermodynamic stability generalizing the Landau criterion for superfluidity are analyzed, and a theory of critical-velocity behavior of superflow is developed. (2) For the two-component system consisting of a lattice and a quasiparticle gas, a two-velocity elasticity theory is developed that explains linear facet growth in helium crystals. (3) For superflow in a uniform gravitational field, the hydrodynamic equations derived by invoking the equivalence principle of general relativity are used to analyze dissipative heat transfer in the Earth’s gravity field.