There is provided a light source device, used in a display device and the like, having a high light emitting efficiency. The light source device has an electric discharge tube containing mercury and electrodes at both ends. A heat conducting member is attached to and is in contact with a part of the electric discharge tube. The heat conducting member locally cools the tube. The heat conducting member and the tube satisfy the following relationship, 6.times.10.sup.-5(m.sup.2k)/S<(1/k1-1/k2)W, where a cross sectional area of the electric discharge tube is S (m.sup.2), an amount of generate heat per unit length of the electric discharge tubes is W (W/m), heat conductivity of the non-cooling part is k1 (W/K/m), and heat conductivity of the cooling part is defined as k2 (W/K/m).