Simulation of dynamic moisture transport processes in building structures under varying conditions re- the solution of the partial differential equations of coupled moisture and heat transport. Our research focuses on the moisture transport equation as this is generally the harder one to solve. We will report on, two related research projects that are motivated by durability-aspects of construction walls, being dependent on specific transport phenomena occurring during operation (first case) and construction (second case). The first case deals with moisture migration as a result of both moisture and tempcrature gradients in concrete walls with a polymer finish. The second case deals with the construction of masonry walls during which the rapid migration of moisture which occurs from the fresh mortar into the bricks has a great effect on the resulting bond strenght of the masonry wall.