The present invention relates to spiroimidazolidine derivatives of the formula I in which E, V, W, X, R1 and R2 have the meanings indicated in the claims. The compounds of the formula I are valuable pharmaceutical active compounds which are suitable, for example, for the therapy and prophylaxis of inflammatory disorders, such as, for example, rheumatoid arthritis, or allergic disorders. The compounds of the formula I are also inhibitors of the adhesion and migration of leukocytes and/or antagonists of the adhesion receptor VLA-4 belonging to the integrins group. They are generally suitable for the therapy and prophylaxis of illnesses which are caused by an undesired extent of leukocyte adhesion and/or leukocyte migration or are associated therewith or in which cell-cell or cell-matrix interactions which are based on interactions of VLA-4 receptors with their ligands play a part. The invention also relates to processes for the preparation of the compounds of the formula I, pharmaceutical preparations which contain compounds of the formula I, and methods for treating these disorders.