Abstract: A constructionally simpler and more reliable pressure-controlled valve device operates with opening pressure which can be switched to low pressure and high pressure on the cooling fluid circuit of an internal combustion engine, partricularly for a motor vehicle. The valve device can be subjected to gas or liquid from inside the cooling fluid container, depending on the operating condition of the engine, and a higher or lower opening pressure is effective depending on the type of pressure load. In such a device, two valves are functionally arranged within one unit such that they are located in parallel and open separately from one another for the different pressure ranges. For this purpose, the closing bodies of the low-pressure valve and of the high-pressure valve are located tightly one upon the other when the high-pressure valve is not open. When the high-pressure valve becomes effective, the flow outlet from the low pressure valve is shut off. It is shut off by a float raised by the cooling fluid.