An apparatus for estimating a valve-clearance that is a minute spacing produced between a valve drive element and a valve element, which when in contact form a moving body of an electro-magnetically operated valve which further includes a pair of electromagnets arranged to be spaced apart from one another via the valve drive element and generating, upon being electrically excited, an electro-magnetic force acting on the valve drive element, and a pair of springs exhibiting a spring force also acting on said valve drive element, said electro-magnetic force and said spring force permitting said valve drive element to move thereby driving said valve element toward either one of valve-closing and valve-opening positions, wherein said moving body includes only said valve drive element when said valve element is not in contact with said valve drive element, said apparatus comprising:
- a position sensing means for determining a position of said valve drive element during a movement of said valve drive element;
- a mass-change estimating means for estimating a change in a mass of said moving body and
- a valve-clearance estimating means for estimating said valve-clearance on the basis of said position of said valve drive element determined by said position sensing means in coordination with the estimate of the change in said mass of said moving body is estimated.