The invention provides a high-pressure discharge lamp incorporating an outer envelope storing a pair of electric terminals a plurality of arc tubes which are respectively stored in this outer envelope and electrically connected in parallel, and a plurality of ignition aids available for assisting operating of these arc tubes, where these ignition aids are provided for each of these arc tubes and contain potentials different from each other. In addition, the invention also provides a lighting system for operating the high-pressure discharge lamp. The lighting system comprises the first and second power supply lines which respectively provides mutual connection between a pair of terminals of the high-pressure discharge lamp, a ballast which is at least provided for either of the first and second power supply lines, a power switch which is provided for either the first or the second power supply line, a pulse generating means which generates either the positive or the negative ignition pulses to be superimposed on AC power voltage output from an AC power supply source, and a control circuit which alters polarity of the ignition pulses output from the pulse generator.