A solenoid-operated valve for use in an internal combustion engine has a valve body movable upwardly for closing an exhaust or intake passage and movable downwardly for opening the exhaust or intake passage, a valve stem extending upwardly from the valve body, a pair of upper and lower solenoids spaced from each other in an axial direction of the valve stem and confronting each other vertically, the valve stem extending through the upper and lower solenoids, a movable plate mounted on the valve stem and disposed between the solenoids, the movable plate being movable between the solenoids to cause the valve stem to open and close the valve body in response to being magnetically attracted by the solenoids, a first spring for normally biasing the valve body to open the exhaust or intake passage, and a second spring for normally biasing the valve body to close the exhaust or intake passage against the first spring. The first spring has a resilient force greater than a resilient force of the second spring. The movable plate is positioned between an intermediate position between the upper and lower solenoids and the lower solenoid when the valve body biased by the first and second springs is in equilibrium.