The movement and morphological change of a solid-liquid interface in directional solidification was investigated during two sounding rocket flights. By using the transparent binary alloy Succinonitrile-Acetone the dynamic processes at the solidification front could be observed directly. Both the planar interface growth, the onset of instability and the characteristic features of the interface morphology, i.e. the evolution of the primary spacing and amplitudes of the cells and dendrites were evaluated. The comparison with a calculation of the morphological instability based on the theoretical model of Warren and Langer showed a good agreement concerning the critical time and velocity of the solidification front.