At least one layer from an oxide-ceramic superconductor material with a high transition temperature is produced on a substrate using a CVD-process. As parent materials, at least one vaporizable composition of each of the metallic components of the superconductor material is provided respectively, and these parent compositions are vaporized respectively at a predetermined temperature and with a predetermined partial pressure. In addition, at least one gaseous coreactant is provided, which is reactive with the parent compositions, the parent compositions as well as a minimum of one coreactant are dosed respectively by means of a carrier gas stream and united in a gas mixture with a predetermined mixture ratio, and to form the superconductor material, the conditions of reaction are adjusted using the energy supply for a reaction of or with the parent compositions and a minimum of one coreactant. A gaseous coreactant containing at least ammonia or organic amines is fed to the gas mixture. Gaseous water is advantageously admixed with this coreactant.