1. A primary air supply system for an internal combusion engine provided with an inlet passage downstream of a throttle valve, said system comprising: a primary air passage connecting an air source and the inlet passage, valve means for opening and closing said primary air passage, said valve means comprising a valve member for opening and closing said primary air passage, a spring urging said valve member to close off said primary air passage, a diaphragm device controlling said valve member, a solenoid valve means opening and closing a pipe in response to switching of an engine control switch with the solenoid valve means opening said pipe when the engine switch is cut off, said diaphragm device having a first diaphragm chamber and a second diaphragm chamber divided by a diaphragm, said first diaphragm chamber being connected to the inlet passage, said second diaphragm chamber being connected to said pipe, said pipe being connected to said second diaphragm chamber at one end and connected to the air source at the other end, whereby, when the engine is decelerating, said diaphragm device opens said primary air passage against said spring as result of high inlet vacuum, and when the engine switch is cut off, the solenoid valve means opens said pipe to introduce air into the second diaphragm chamber so that said diaphragm device opens said primary air passage by a difference of pressure between said chambers.

3. A primary air supply system for an internal combustion engine provided with an inlet passage downstream of a throttle valve comprising: a. a primary air passage connected between an air source and the inlet passage, b. first detecting means for detecting the engine decelerating condition, c. second detecting means for detecting the cut-off of an ignition switch, d. normally closed valve means disposed on said primary air passage and operatively connected with said first and second detecting means for opening said passage in response to cutting off the ignition switch and deceleration of the engine.