A simultaneous solution procedure for fluid-structure interaction problems in the area of building aeroeiasticity is presented.,The structural motion is described by a geometrically nonlinear theory for elastic deformation behavior using a total Lagrangian approach. The flow field is modeled by the incompressible Navier-Stokes equations, which will be Reynolds averaged, if turbulence effects are essential In this case, the k-w turbulence model of Wilcox is used. The space-time finite element method is applied to both continua leading to a consistent discretization of fluid and structure. Since isoparametric space-time elements are adaptable in time direction, the method implies a natural description of the time dependent fluid domain, which has moving boundaries as a result of structural deformations. In order to enforce momentum conservation between both continua, a weighted residual formulation of coupling conditions is introduced using boundary tractions as additional variables. Numerical investigations of aeroelastic instabilities of bridge deck cross sections and flutter phenomena of gravity prestressed membranes demonstrate efficiency and versatility of the numerical scheme, which ensures high convergence and accuracy due to the simultaneous solution of the strongly coupled system.