To provide an exhaust gas treating device capable of preventing sticking of a byproduct by heating the inside of a byproduct collecting device in the beginning of an introduction of the exhaust gas, and its operation method.

In the exhaust gas treating device by which sulfur oxide and/or nitrogen oxide in the exhaust gas are converted into a powdery reaction byproduct by introducing the exhaust gas into a reactor 4, adding ammonia 13, irradiating with electron-beams 5, and are collected with the byproduct collecting device 7, a heat exchanger 6 for adjusting the temperature of the exhaust gas is provided between the reactor 4 and the byproduct collecting device 7. The heat exchanger 6 can have a heat medium switching mechanism for switching steam or hot water to cool water as the heat medium. Also, the heat exchanger 6 is inserted a partitioning plate and/or an inner partitioning wall inside a duct reaching from the reactor 4 to the byproduct collecting device 7, and the contact surface can be used as a heat exchange surface, and it may have a structure having a flow path for allowing the heat medium to flow in the inside.