One-dimensional quantum liquids are commonly treated using the Luttinger liquid theory, which neglects elementary excitations with high energies. In this approximation, in addition to the number of particles, energy, and momentum the liquid possesses another conserved quantity - J, which may be interpreted as the difference between the numbers of right- and left- moving particles. Beyond the Luttinger liquid approximation J is no longer conserved, but its relaxation time is exponentially long at low temperatures. I will show that as a result, one-dimensional quantum liquids exhibit two-fluid behavior. In particular in a wide frequency interval they support two sound modes that are similar to the first and second sound in superfluid He.