Electromagnetic surface waves are investigated propagating on the planar interface between unmagnetized warm two-fluid plasmas of different densities and between a magnetized warm plasma and free space. The most general forms of the dispersion relations are obtained in closed forms and various limiting cases are discussed. In particular, the influence of a cold plasma on the surface ion acoustic wave is analysed. Also the dispersion relation of an electrostatic surface wave is solved in detail propagating on the interface between vacuum and a warm plasma with a static magnetic field directed along the interface and perpendicular to the wavevector.