Process and apparatus for continuous casting in a twin-belt casting machine in which the moving side dams are guided along opposite sides of the moulding cavity by guide device extending along beside the respective moving side dams, and the moving side dams are cooled by cooling fluid circulated in at least a part of the guide device and applied directly to the moving side dams. The moving side dams are cooled by cooling fluid sprayed through orifices in the guide device directly onto the moving side dams along at least a part of the downstream zone of the moulding cavity. During movement of the side dams along the moulding cavity from its entrance to its exit, they pass successively through a first (or upstream) zone in which they face molten metal and through a second (or downstream) zone in which they face solidified metal. The cooling fluid is sprayed directly onto the moving side dams only in this second zone. The first zone occupies from approximately 3/10ths to approximately 1/2 of the overall length of the moulding cavity, and the second zone occupies the remainder. The cooling fluid is advantageously sprayed directly toward the side dam for providing very effective cooling action, and this cooling fluid is aimed in a downstream direction that forms an acute angle with the moving direction of the side dam. Preferably this acute angle is in the range from approximately 20.degree. to approximately 50.degree. for propelling the cooling fluid downstream away from the first zone, and preferably the cooling fluid is water.