Abstract: There is provided a slagging coal combustion system suitable for retrofitting boilers, furnaces and industrial-process heat generators originally designed to burn oil or gas. It comprises a primary combustion chamber into which oxidizer and fuel are injected to provide high-velocity, rotational-flow combustion zones, such that the fuel is burned substoichiometrically, while in flight, with up to 90% of the resultant ash being removed as molten ash. The combustion products pass from the primary chamber to chamber where slag is removed and the gaseous products are passed to end-use equipment. A coal-fired precombustor subsystem feeds partially-heated air as the oxidizer to the primary combustion chamber supply of oxidizer, at any selected temperature within the range from about 1200.degree. F. to about 2000.degree. F. The stoichiometry of this precombustor and the velocity and mass-flow rates of its output stream are independently controllable.