The invention pertains to a process for stripping conductor traces (2) of extruded or laminated flat cables (1), so-called FFCs, using laser beams (4).The invention is characterized in that a beam of a CO.sub.2 laser or an Nd:YAG laser (4) is used in a first step, and an excimer laser or a frequency-multiplied Nd:YAG laser is used in a second step, in that the CO.sub.2 laser or Nd:YAG laser is allowed to act on the extrudate (3) of FFC (1) with an intensity and duration such that an extrudate layer (6) a few microns thick still remains in the area of the conductor trace(s) (2), said layer being removed in the second step by the beam of the excimer laser or frequency-multiplied Nd:YAG laser.