The invention relates to a sequence casting process for producing a high-purity cast metal strand from a metal melt, the metal melt being fed in controlled fashion from a metal vessel to a tundish and being discharged in controlled fashion from this tundish into a continuous-casting mold, and the supply of the metal melt into the continuous-casting mold being continued without interruption. To allow a high-quality metal strand to be cast even during the change of melt vessel in this process, with the restart phase being kept as short as possible, it is proposed that during a period of time from the resumption of the supply of metal melt into the tundish until the point at which a quasi-steady operating bath level in the tundish is reached, the inflow rate into the tundish is greater than the outflow rate out of the tundish, and for 70% to 100% of this period the inflow rate into the tundish is less than or equal to double the outflow rate out of the tundish.