The present invention relates to cinnamoylaminoalkyl-substituted benzenesulfonamide derivatives of formula Iin which A(1), A(2), A(3), R(1), R(2), R(3), R(4), X, Y, and Z have the meanings indicated in the claims. Compounds of formula I are valuable pharmaceutical active compounds which exhibit, for example, an inhibitory action on ATP-sensitive potassium channels in the cardiac muscle and/or in the cardiac nerve and are suitable, for example, for the treatment of disorders of the cardiovascular system such as coronary heart disease, arrhythmias, cardiac insufficiency or cardiomyopathies, or for the prevention of sudden cardiac death, or for improving decreased contractility of the heart. The invention furthermore relates to processes for the preparation of compounds of formula I, their use, and pharmaceutical preparations comprising them.