NOVELTY - The method involves selecting one exhaust gas processing mode, in which the fuel is ignited by a glow plug (30) and introduced from the bypass passage (31a) to an exhaust emission purifier (25), when determined that flame failure at time of fuel ignition is absent, or another exhaust processing mode, in which fuel is supplied from an exhaust passage (22a) to the purifier via the exhaust turbine (24b) without igniting the fuel, when determined that flame failure is present.    USE - Method for processing exhaust gas introduced into exhaust emission purifier in vehicle-mounted internal combustion engine, such as compression-ignition internal combustion engine.    ADVANTAGE - Time for warming-up the exhaust emission purifier at cold condition can be shortened, omitting use of a secondary air supply source. The active state of the exhaust emission purifier is maintained by using the fuel supplying valve and glow plug even when the engine is operating. High temperature exhaust gas can be efficiently introduced into the purifier by selecting one exhaust gas processing mode in which fuel ignition is possible. The fuel can be supplied in uniformly dispersed state into the purifier via the exhaust turbine by selecting the other processing mode in which fuel ignition is impossible. Fuel may not be supplied to the purifier when the exhaust gas temperature exceeds a given temperature, avoiding wasteful fuel consumption.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for an apparatus, in which an exhaust turbocharger and an exhaust emission purifier are incorporated, for processing exhaust gas introduced from an internal combustion engine to the exhaust emission purifier.    DESCRIPTION OF DRAWING(S) - The drawing shows the outline of an exhaust gas processing apparatus applied to a compression ignition internal combustion engine.    Exhaust passage (22a)    Exhaust turbine (24b)    Exhaust emission purifier (25)    Glow plug (30)    Bypass passage (31a)