An ignition system for internal combustion engines, has a plurality of spark plugs, an ignition coil provided for the spark plugs and having a secondary circuit, at least one trigger diode cascade formed as a high voltage semiconductor switch and connected in the secondary circuit of the ignition coil prior to each of the spark plugs so as to change suddenly from a blocking state to a conducting state at a preselected voltage for generating ignition sparks, and a capacitor connected parallel to the secondary winding of the ignition coil between the ignition coil and the trigger diode cascade.