Based on the energy, mass and momentum conservation laws, a system of coupled non-linear transport equations including a suitable computer code has been developed to determine the temperature, moisture, ice, vapour pressure, air pressure fields and the heat, enthalpy, vapour, water and air flows in porous building materials and in building structures under conditions of use. The contribution demonstrates the thermohygric behaviour of a typical heavy concrete flat roof with a mineral wool insulation layer, the drying out process of an insulated light-weight wooden roof caused by a capillary-active vapour barrier, the moisture and temperature field in an air permeable building component, and the impact of a capillary-active inside insulation of a framework-house (exposed timber) being thermally renovated right now.