A valve opening and closing timing control apparatus comprising: a driving-side rotational member rotating synchronously with a crankshaft of an internal combustion engine about a rotation axis of the driving-side rotational member; a driven-side rotational member arranged coaxially with the rotation axis of the driving-side rotational member and rotatable relative to the driving-side rotational member, the driven-side rotational member rotating integrally with a camshaft for opening and closing a valve of the internal combustion engine; and a phase adjustment mechanism specifying a relative rotational phase between the driving-side rotational member and the driven-side rotational member by an electric actuator, the phase adjustment mechanism including a ring gear arranged coaxially with the rotation axis, the ring gear including internal teeth and serving as the driven-side rotational member, an inner gear arranged coaxially with an eccentric axis which is in parallel with the rotation axis, the inner gear including external teeth of which number is different from a number of teeth of the ring gear, and a linkage mechanism which brings the inner gear to be linked to the driving-side rotational member, the phase adjustment mechanism being constructed as a differential deceleration mechanism where the inner gear is rotated relative to the ring gear by revolution of a position of the eccentric axis with reference to the rotation axis by a driving force of the electric actuator in a state where a part of a teeth portion of the ring gear is meshed with a part of a teeth portion of the inner gear, the linkage mechanism being constructed by including a coupling member at which a first engagement portion engaging with the driving-side rotational member in a displaceable manner in a first direction serving as a radial direction and a second engagement portion engaging with the inner gear in a displaceable manner in a second direction orthogonal to the first direction are integrally provided on an imaginary plane orthogonal to the rotation axis. a driving-side rotational member rotating synchronously with a crankshaft of an internal combustion engine about a rotation axis of the driving-side rotational member; a driven-side rotational member arranged coaxially with the rotation axis of the driving-side rotational member and rotatable relative to the driving-side rotational member, the driven-side rotational member rotating integrally with a camshaft for opening and closing a valve of the internal combustion engine; and a phase adjustment mechanism specifying a relative rotational phase between the driving-side rotational member and the driven-side rotational member by an electric actuator, the phase adjustment mechanism including a ring gear arranged coaxially with the rotation axis, the ring gear including internal teeth and serving as the driven-side rotational member, an inner gear arranged coaxially with an eccentric axis which is in parallel with the rotation axis, the inner gear including external teeth of which number is different from a number of teeth of the ring gear, and a linkage mechanism which brings the inner gear to be linked to the driving-side rotational member, the phase adjustment mechanism being constructed as a differential deceleration mechanism where the inner gear is rotated relative to the ring gear by revolution of a position of the eccentric axis with reference to the rotation axis by a driving force of the electric actuator in a state where a part of a teeth portion of the ring gear is meshed with a part of a teeth portion of the inner gear, the linkage mechanism being constructed by including a coupling member at which a first engagement portion engaging with the driving-side rotational member in a displaceable manner in a first direction serving as a radial direction and a second engagement portion engaging with the inner gear in a displaceable manner in a second direction orthogonal to the first direction are integrally provided on an imaginary plane orthogonal to the rotation axis.