We consider a one component system of coexisting liquid and vapor phases with a diffuse planar interface and investigate the transport properties along the interface. We start with a formally exact, coupled set of generalized Langevin equations for the fluctuations in the number density, momentum density, energy density, stress tensor, and heat flux in an inhomogeneous fluid. We use these equations to calculate the transverse current-current correlation function RT for the liquid-vapor system. In contrast to homogeneous fluids, RT depends on the nonlocal viscoelastic properties (even in the long wavelength limit). These viscoelastic properties are related to "shearing" and "stretching" of the interface. The calculation of RT indicates a natural way of introducing nonlocal elastic moduli and nonlocal frequency dependent viscosities for inhomogeneous systems. © 1982 American Institute of Physics.