The invention relates to a gas supply device for delivering precursors with a low vapor pressure to CVD coating systems. Said gas supply device has a supply container for the precursor which is at a first temperature T1, an intermediate storage device for intermediately storing the vaporous precursor at a second temperature T2 and at a constant pressure p2, a first gas line between the supply container and the intermediate storage device and a second gas line for removing gas from the intermediate storage device. According to the invention, the gas supply device is developed in such a way that the first temperature T1 is higher than the second temperature T2. The lower temperature T2 of the intermediate storage device facilitates maintenance work on the same, while the precursor evaporates at a greater rate at the higher temperature T1 in the supply container. According to a particularly advantageous embodiment, a first precursor vapor is mixed with a gas and/or a second precursor vapor in the intermediate storage device. The partial pressure of the first precursor vapor in the intermediate storage device is lower than that of the undiluted first precursor vapor at a constant overall pressure in said intermediate storage device, so that the temperature T2 of the intermediate storage device and the successive lines can be reduced. Reducing the temperature T2 allows less expensive components to be used.