A variable valve operating system assembled in an engine includes a first rocker arm contacting with a valve, a second rocker arm no contacting with any valve, a lost motion spring bringing the second rocker arm into contact with a cam, and switching device for switching the first/second rocker arms to a coupled or uncoupled state. An operation control apparatus for the engine includes element for determining whether or not an engine speed is higher than a first speed at which supply of fuel is allowed to be temporarily stopped, and element for setting a requested quantity of increase/decrease in internal resistance of the engine. When the engine speed is higher than the first speed and an accelerator opening degree is 0%, the switching device switches the first/second rocker arms to the coupled or uncoupled state based on the requested quantity.