A pulse generating circuit for a plasma ignition system includes a thyristor (32) connected between a supply terminal (21a) and earth. A primary winding (Wp) of a transformer (TR) and a first capacitor (C I ) are connected across the thyristor (32). The supply terminal (21a) is also connected through a secondary winding (W.) and a diode (D) to an output terminal (21c). A saturable core inductor (L) and a second capacitor (C 2 ) are connected in series across the output terminal (21c) and earth. A plasma plug (15) is also connected across the output terminal and earth. In operation, the first and second capacitors are charged and the thyristor (32) is fired. A high voltage pulse is applied by the secondary winding (W 2 ) to the plasma plug (15) causing electric breakdown. The second capacitor (C 2 ) then discharges through the inductor (L) and the plasma plug (15). Four alternative circuits are also described.