An apparatus and a method serving for electrochemically polishing and/or pickling the inner surfaces (16) of pipes (10) provide for a polishing head (12) to be moved through the pipe. The polishing head (12) comprises a dielectric outer wall which defines a narrow working gap (28) together with the inner pipe surface (16) to be cleaned, the electrolyte flowing through said gap. This permits electrochemical polishing of high quality of the inside surface of the pipe with little consumption of electrolyte. The electrolyte stream may be divided into cathodic and anodic partial streams (30 and 32, respectively