for a rocker arm in which pivotal support is made between the distal part of the arm and a push rod moreover in the second embodiment the ball like portion 116 may be simply held with a spherical concave surface in a slip off preventing manner without being pressed thereagainst it should be well noted that according to the foregoing embodiments both the ring like member 18 of u form and the clip member 118 of c form are elastically expansive and contractive in the radial directions thereof so that in the assembly or disassembly work they can be attached or removed with small forces referring to fig5 description will now be made of a third embodiment of the present invention in this embodiment for a rocker arm 214 cooperating with a push rod 220 to constitute a valve operating mechanism while the rocker arm 214 is rockably mounted at the longitudinally central part thereof through a support shaft 221 on a cylinder head there is provided a pivotal mechanism disposed between the rocker arm 214 and the push rod 220 which pivotal mechanism also has a ball like portion 216 engaged in a spherical concave portion 212 and an elastic member 218 fitted at the aperture end of the spherical concave portion 212 as will be understood from the foregoing description according to the present invention in a pivotal structure of a rocker arm a ball like portion is elastically pressed against a spherical concave portion to obtain resiliently oppressive contact between a spherical convex surface.