Heilbronner in 1964 predicted that annulenes with ".. a planar perimeter of N=4r AO's, which would yield an open shell configuration when occupied by 4r electrons, can be twisted into a closed shell Möbius strip perimeter without loss in pi electron energy". We have been able to synthesize the first [4n]annulene with such a Möbius topology and now present further Möbius isomers and the details of their preparation as stable compounds. To address the question whether the twist in the pi system has an effect on the properties we systematically investigate energy, geometry and magnetic parameters of a large number isomers of annulenes. The Möbius twisted annulenes are consistently more aromatic than the non-twisted isomers. This is true for the parent as well as our benzoannelated systems. Our results are in contrast to those published recently by C. Castro, W. L. Karney, P. von R. Schleyer et al.