Abstract: A machine is provided for the multiple-pass dyeing of cord fabrics. The machine includes a dyeing vat containing at least two Overflow or Jet units or funnels, arranged adjacent to each other and associated with at least two reels straddling at least two fabric collecting vats and the at least two Overflow or Jet units or funnels (24-29), so as to pick up the cord fabric contained in the collecting vats and introduce the cord fabric into the Overflow or Jet funnels. The cord fabric is tied into a ring. For the purposes of passing the cord fabric, the collecting vats and Overflow or Jet funnels are connected to each other in a non-sequential manner and in a number lower than the maximum number of fabric collecting vats and Overflow or Jet units or funnels present in the machine. Moreover, in machines equipped with at least four compartments, two of the fabric collecting vats and the Overflow or Jet units or funnels, located next to the opposite ends of the dyeing vat, are connected to each other in series.