A vehicle cooling system includes a first fan assembly, a second fan assembly, and a control unit. The first fan assembly generates a main cooling flow acting upon a first cooler arrangement. The second fan assembly generates a secondary cooling flow adjacent to the main cooling flow and acting upon a second cooler arrangement. The secondary cooling flow is branched off from the main cooling flow via the second fan assembly. The main and secondary cooling flows pass through a filter element located upstream of the first and second fan assemblies and the first and second cooler arrangements. The control unit is configured to determine an actual value of a rotational speed variable of the second fan assembly, compare the actual value with a desired value specified for a cleaned state of the filter element, and generate a trigger signal to initiate a reversing operation of the first fan assembly.