Here is disclosed a combustion system for sooty smoke generating facilities allowing combustion exhaust gas generated from incineration of various types of garbage to be continuously composition-analyzed so that, based on the analytical result, an operating condition of a combustion furnace may be changed and/or said combustion furnace may be supplied with suitable neutralizers and thereby air polluting substances contained in the exhaust gas may be rapidly collected, and allowing a dust collecting efficiency with which a dust collector is collecting the air polluting substances or the other substances to be continuously measured so that a proper timing for cleaning of the dust collector and/or part-exchange may be reliably determined. There is provided at a measuring spot A adjacent an outlet of a garbage incinerating furnace 1 a collecting duct 7a in communication with an infrared spectroscopic analyzer 10 into which the combustion exhaust gas is introduced for composition-analysis. Analytical result is transmitted to control means 12. When air polluting substances higher than predetermined values are contained in the exhaust gas, the control means 12 applies neutralizer supplying means 13 and operating condition readjusting means 14 with control signals instructing these means to take necessary countermeasures. In response to such instructions, the neutralizer supplying means 13 supplies the garbage incinerating furnace 1 with appropriate neutralizers to neutralize these undesirable substances and the operating condition readjusting means 14 controllably readjusts operating condition of the incinerating furnace 1, for example, combustion temperature and combustion time period of the incinerating furnace 1 and turbulence condition during combustion. The exhaust gas sampled at a measuring spot B along a flue 6b is introduced into the analyzer means 10 for composition-analysis and it is determined whether the exhaust gas to be emitted into the atmosphere contains the air polluting substances or not. A ratio between concentrations of a given substance determined at the measuring spot A and determined at the measuring spot B is calculated to determine a variation in the dust collecting efficiency of the dust collector 3.