The characteristics of electromagnetic surface waves supported by a plane interface separating a semi‐infinite region of free space from another semi‐infinite region consisting of a plasma streaming parallel to the interface are investigated for the case in which the wave is progressing either in or opposite to the direction of the stream. The behavior of the surface wave is drastically different from the case in which the plasma is stationary. The surface wave has backward‐wave regions. For a certain range of frequencies below the plasma frequency, the surface wave undergoes traveling wave amplification in the direction of the stream. When its wave number is in a certain range, the surface wave progressing in a direction opposite to that of the stream is convectively unstable. The characteristics of this surface wave instability are analyzed.