The structure of moving domain walls in thin films having a uniaxial anisotropy axis in the plane of the film is calculated by a variational method. The calculation applies for wall velocities &ngr; smaller than a critical velocity at which the derivative of the wall energy with respect to &ngr; becomes infinite. At intermediate film thicknesses the critical velocity is much smaller, the effective wall mass (per unit area) much larger than for bulk crystals and/or very thin films.