A mold-supporting system for a machine for forming hollow glassware, includes a supporting structure, a first carriage and a second carriage, which are slidably mounted respectively on a first bar and a second bar of the supporting structure, and carry, respectively, a first mold-carrier arm and a second mold-carrier arm. A mutual displacement of the first and second carriages between a position where they are set close to one another and a corresponding position where they are set apart is controlled. On one between the first and second carriages, means are provided for guiding the other between the first and second carriages during their mutual displacement.