A compression ignition internal combustion engine comprising a combustion chamber to which air and fuel are supplied, an intake valve for opening and closing a passage between said combustion chamber and intake port communicating with said combustion chamber, and an exhaust valve for opening and closing a passage between said combustion chamber and an exhaust port communicating with said combustion chamber, the temperature and pressure in said combustion chamber being increased to self-ignite an air-fuel mixture with the compressive operation of a piston after closing of said intake valve, wherein said compression ignition internal combustion engine further comprises: auxiliary fuel injecting means for injecting an auxiliary fuel directly into said combustion chamber at an arbitrary timing in a state in which said intake valve and said exhaust valve are closed, depending an operating conditions of said compression ignition internal combustion engine so that an air-fuel mixture under a compression or expansion stroke of the piston is brought into an ignitable state, and control means for controlling at least one of an injection timing, an injection amount, and an injection pressure of the auxiliary fuel depending on the operating conditions, wherein said compression ignition internal combustion engine further includes a variable valve mechanism (15a,15b) for varying a valve timing of at least one of said intake valve and said exhaust valve, and wherein said variable valve mechanism (15a,15b) is controlled to give rise to a state in which said intake valve and said exhaust valve are both closed during an exhaust stroke, thereby causing burnt gas at a high temperature to remain in the combustion chamber, and the auxiliary fuel is injected into the remaining gas, wherein said compression ignition internal combustion engine includes an ignition timing detecting device for detecting a self-ignition timing of the air-fuel mixture, characterized in that the ignition timing detecting device is adapted that when a detection result of said ignition timing detecting device is advanced from a target ignition timing, said control means makes control to reduce an injection amount of the auxiliary fuel or to delay the injection timing of the auxiliary fuel, and that when a detection result of said ignition timing detecting device is delayed from a target ignition timing, said control means makes control to increase an injection amount of the auxiliary fuel or to advance the injection timing of the auxiliary fuel; wherein said compression ignition, internal combustion engine includes an ignition device for performing the engine operation with spark ignition, and wherein injection of the auxiliary fuel is inhibited in a spark ignition combustion mode, into which the engine operation is selectively switched from the compression ignition combustion mode depending on the drivers intention and the engine load, wherein the drivers intention is calculated from an accelerator opening and a brake depressing force, and wherein the engine load is determined based on vehicle traveling conditions and engine operating conditions. auxiliary fuel injecting means for injecting an auxiliary fuel directly into said combustion chamber at an arbitrary timing in a state in which said intake valve and said exhaust valve are closed, depending an operating conditions of said compression ignition internal combustion engine so that an air-fuel mixture under a compression or expansion stroke of the piston is brought into an ignitable state, and control means for controlling at least one of an injection timing, an injection amount, and an injection pressure of the auxiliary fuel depending on the operating conditions, wherein said compression ignition internal combustion engine further includes a variable valve mechanism (15a,15b) for varying a valve timing of at least one of said intake valve and said exhaust valve, and wherein said variable valve mechanism (15a,15b) is controlled to give rise to a state in which said intake valve and said exhaust valve are both closed during an exhaust stroke, thereby causing burnt gas at a high temperature to remain in the combustion chamber, and the auxiliary fuel is injected into the remaining gas, wherein said compression ignition internal combustion engine includes an ignition timing detecting device for detecting a self-ignition timing of the air-fuel mixture, characterized in that the ignition timing detecting device is adapted that when a detection result of said ignition timing detecting device is advanced from a target ignition timing, said control means makes control to reduce an injection amount of the auxiliary fuel or to delay the injection timing of the auxiliary fuel, and that when a detection result of said ignition timing detecting device is delayed from a target ignition timing, said control means makes control to increase an injection amount of the auxiliary fuel or to advance the injection timing of the auxiliary fuel; wherein said compression ignition, internal combustion engine includes an ignition device for performing the engine operation with spark ignition, and wherein injection of the auxiliary fuel is inhibited in a spark ignition combustion mode, into which the engine operation is selectively switched from the compression ignition combustion mode depending on the drivers intention and the engine load, wherein the drivers intention is calculated from an accelerator opening and a brake depressing force, and wherein the engine load is determined based on vehicle traveling conditions and engine operating conditions.