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This paper deals with the investigation of an electrical discharge propagated along a thin liquid jet. The propagation modes were studied. Three discharge areas were found out. The continuous degenerated glow discharge between an electrode and jet appeared at small current lower than ~5 mA and then transformed into a sliding surface pulse discharge propagated along the jet by increasing the current. The relative discharge pulse period was inversely proportional to the transit time for the jet. The surface discharge degenerated to an arc over the jet at a current above 20 mA. The surface discharge area was narrowed down at the increase of the electrical conductivity of liquid.