The alignment behaviour of molecules has been in the focus of experimental and theoretical work for around 15 years. Still our 3D calculations for nitrogen and hydrogen molecules showed unknown behaviour. So, we found an unexpected difference between the hydrogen molecular ion and the hydrogen molecule, i.e. the fragments from the ion are perfectly aligned for a large range of intensities while those from the neutral molecule are not. In N₂ a completely different geometric alignment was observed which nevertheless is consistent with existing experimental observations.