A continuous-casting unit produces a longitudinally extending and traveling strand having a solid shell and a liquid core. A strand-guiding apparatus has a plurality of longitudinally spaced section frames and respective pairs of roller assemblies carried on the frames and transversely flanking and bearing transversely on the strand. Each pair forms a gap through which the strand passes, and each roller assembly is formed by two aligned subrollers. A respective center is provided bearing between the subrollers of each roller assembly and bracing inner ends of the respective subrollers transversely against the respective frame. Respective outer rollers at outer ends of the subrollers of each roller assembly brace the respective outer ends transversely against the respective frame. The subrollers are shaped or supported on the respective frame such that in an unloaded condition the gap is transversely narrower at the center bearing than at the outer bearing.