A valve operating system for an internal combustion engine includes a valve-opening electromagnet and a valve-closing electromagnet for exhibiting an electromagnetic force for attracting an armature to operate an engine valve, and a valve-opening resilient means and a valve-closing resilient means for maintaining the armature at a predetermined neutral position during deenergization of the electromagnets. In each electromagnet, a coil is inserted between inner and outer yokes which are disposed in the form of a double-cylinder such that they open at their ends opposed to the armature and are magnetically coupled to each other at their ends opposite from the armature, and the coil is positioned so that the coil protrudes from at least one of the yokes toward the armature. The armature has an annular accommodating portion provided in a surface thereof opposed to each the electromagnets and capable of accommodating that portion of the coil which protrudes from the yoke. With such a structure, it is possible to increase the electromagnetic attracting force of each of the electromagnets and to enhance the performance of the engine.