The paper describes interrelated electromechanical systems of the continuous sub-train of the wide-strip hot-rolling mill (WSHRM). It notes peculiarities of interrelation of edging and horizontal rolls of the universal train that result in the repeated transient process within the electromechanical systems of edging rolls at strip gripping by horizontal rolls. It justifies the need for developing means to control electric drives of the universal stand providing limitation of their dynamic currents in this transient mode. The paper proposes a conceptual approach at which dynamic loads are limited due to consistent coordination of speed of the strip leaving rolls of the previous stand and linear one of the next stand with transfer of the control action in the rolling direction. It considers the methods for control of speed modes of electric drives installed at the continuous WSHRM sub-train than ensures implementation of this approach. A static error of speed control and dynamic torque of the electric motor of the next stand formed at strip gripping may be compensated by means of high-speed non-corresponding control of electric drive of the previous stand. The study provides outcome of study of the above methods by means the developed mathematical model of the interrelated stands of the rouging continuous WSHRM train. It is proven that the proposed method of speed mode control helps to establish the best possible roll speed relation before strip grip. Based on the comparison of transient processes within the existing system of the electric drive control and those in the system implementing the methods developed, the study confirms that dynamic current of the edging roll motor may reduced by ±10 %. At this, there is practically no looping at the side of horizontal rolls at simultaneous rolling. It provides recommendations for commercialization of these technical solutions.