Apparatus and method for controlling a vehicle power supply network

The method involves regulating the on-board system voltage (UN) with a high rate of increase while the voltage is less than a defined threshold value after connecting a load and regulating the voltage with a low rate of increase if the voltage has increased above the threshold again. The voltage is regulated in accordance with a load-response function if it is above the threshold. An independent claim is also included for the following: (a) a device for regulating an on-board electrical system for a motor vehicle.