Abstract: Liquid-conveying pipelines are tested for leaks during inoperative periods. To this end, the pipeline is hermetically closed at its two ends and the pressure prevailing in the interior of the pipeline is continuously measured. Once the pressure prevailing therein is found to drop, a substitute liquid is conveyed through the pipeline in the quantity necessary to make up for that decrease in volume of the normally conveyed liquid which is caused by the relevant temperature drop, an alarm device is actuated if the pressure continues to drop, and the magnitude of the leak is ascertained as an inference from the quantity of substitute liquid introduced per unit time into the closed pipeline.