Abstract: In the operation of a continuous-process annealing furnace for a steel strip of a continuous length which is guided through the high-temperature zones of the furnace by the upper and lower hearth rolls in an alternate up and down vertical movement, each of the hearth rolls having an end-tapered or crowned configuration to correct the meandering of the running strip, each of the hearth rolls is coupled with one or a plural number of straightly cylindrical auxiliary rolls in contact with the strip at a position close to the hearth roll. By virtue of the installation of the auxiliary rolls, the phenomenon of wrinkling or buckling in the steel strip can be effectively prevented without causing meandering and the effect is more remarkable when specific relationships are held among the values of the diameters of the hearth roll and auxiliary roll and the position of the auxiliary roll relative to the hearth roll.