While the transfer equations for moisture and heat in building components are currently undergoing standardisation, atmospheric boundary conditions, conservative modelling and numerical efficiency are not addressed. In a first part, this paper adds a comprehensive description of those boundary conditions, emphasising wind-driven rain and vapour exchange, the main moisture supply and removal mechanism, respectively. In the second part the numerical implementation is tackled, with specific attention to the monotony of the spatial discretisation, and to the mass and energy conservation of the temporal discretisation. Both issues are illustrated with exemplary hygrothermal simulations. Numerical efficiency is treated in two follow-up papers. (c) 2006 Elsevier Ltd. All rights reserved.