1. A process for the control of secondary cooling of elongate workpieces leaving a forming stage of a continuous-casting machine, comprising the steps of: (a) effecting the cooling by jets of a cooling fluid trained at several cooling zones upon a workpiece traversing same; (b) modifying the cooling fluid flow in response to variations in the casting speed of the advancing workpiece; (c) generating a value of a fictitious speed, taking into account expected speed changes due to a foreseeable event, lying between a measured real-time speed and an anticipated speed, and substituting said fictitious speed for said real-time speed in the computation of an average speed at each cooling zone, said anticipated speed being an advance image of a significant variation of future speed expected within a lead time, said cooling fluid flow being modified in step (b) at least in part in response to said computation of said average speed.