The Rayleigh-Benard convection with a superimposed horizontal shear flow in rectangular domains is treated numerically utilizing a finite difference method and experimentally by applying an interferometric measuring technique. The fluid used is silicon oil, a high Prandtl number fluid, Pr = 530, The investigations concern the supercritical Rayleigh number region of 2300 less than or equal to Ra less than or equal to 20 000. The Reynolds number, which characterizes the strength of the throughflow, varies in the range of 3 x 10(-5) less than or equal to Re less than or equal to 0.1. According to special parameter combinations of the Rayleigh and the Reynolds number, convective rolls with different orientations can be distinguished. The dynamical behavior of travelling, transverse rolls is also considered.