In a motor-driven power steering apparatus for converting rotation of an
electric motor into a linear stroke of a rack shaft by an interposition
of a power transmission mechanism and steering a tire wheel connected to
the rack shaft, there is provided a motor slip detecting means for
previously determining a cumulative rotational speed of the electric
motor corresponding to a maximum stroke displacement amount of the rack
shaft, integrating the rotational speed of the electric motor, and
estimating that slip or idle running is generated in a rotational force
transmission system from the electric motor to the rack shaft, where the
integral rotational speed of the electric motor becomes more than a
prescribed cumulative rotational speed.