The infrared sensor systems AVHRR (Advanced Very High Resolution Radiometer) and HIRS (High resolution Infrared Radiation Sounder) on board the NOAA-7 satellite are studied theoretically by means of radiative transfer calculations to enable the development of new retrieval techniques for atmospheric water vapour profiles. Simulations of radiometer signals have been performed for a large set of atmospheres from the middle and tropical latitudes. Subsequent development of a physical-statistical retrieval method demonstrates the usefulness of a coupling of both radiometers for water vapour retrievals in a single HIRS field of view. Total column amounts as well as the amounts in thick layers (150-200 hPa (thick) in the lower troposphere can be derived with an accuracy of 5-15 per cent and 15-25 per cent respectively. The amounts in thinner layers (50hPa) can be estimated with accuracies between 20 and 30 per cent. The AVHRR split window channels are a powerful tool in the water vapour retrievals. The technique developed benefits from the simultaneous retrieval of temperature profiles and surface temperatures. Accounting for scan-angle dependencies explicitly leads to improved retrievals. The synergy of AVHRR with HIRS increases the number of retrievals in partially cloudy fields of view compared with HIRS retrievals alone. A case study demonstrates the capability of the method to resolve water vapour structures with a high spatial resolution and its value in areas where conventional measurements from radiosonde ascents are sparse.