Based on the energy, mass and linear momentum conservation laws as well as the entropy law, a coupled, partial, non-linear, differential equation system for the heat, air and moisture transfer in porous materials follows, and for the more-dimensional solution of it, a suitable algorithm including the simulation software has been developed. Its efficiency is demonstrated by a recent building structure - chuted concrete between fibre board with polystyrol-foam outside insulation - under the boundary conditions of the TRY Essen : hourly values of outdoor climate. As a result of the high built-in moisture, moisture damages (mould growing) in the base level (exterior wall/concrete plate over the basement garage) and inadmissible high heat losses caused by the moisture depending thermal conductivity and the additional enthalpy flows coupled to the moisture movement and phase changing are observed in the first years.