To prevent the delay in fuel shut-off prohibition control because of a delay in detecting the temperature of catalysts, and also prevent components in an exhaust system from being damaged because of abnormal over-heating by estimating the maximum catalyst temperature obtained under the condition beforehand, and furthermore computing an estimated value for the temperature of catalysts.

In a device equipped with an engine torque reducing means (b) which cuts off fuel feed to the respective cylinders of an engine, and thereby reduces engine torque, the maximum catalyst temperature obtained under the condition is forecasted based on the cut-off quantity of fuel feed by the aforesaid means (b) and the quantity of intake air by an intake air quantity detection means (c), the aforesaid forecasted temperature is multiplied by a delay correction caused by a delay time constant, and an estimated value for the temperature of catalysts is thereby computed (d). When the acceleration slipping condition of each driving wheel is detected (a) by an acceleration slipping control means (e), and when the estimated value of catalyst temperature is less than a specified catalyst protection temperature, let torque reducing control be executed, meanwhile, when the estimated value of catalyst temperature is equal to or more than the specified catalyst protection temperature, the cut-off quantity of fuel feed is thereby reduced so as to be corrected.