A valve train of an internal combustion engine comprising a tappet and a hollow tappet pushrod that is actuated by said tappet, said tappet pushrod comprising on one end, a first support for an at least indirectly contacting pressure piston of a hydraulic lash adjuster of said tappet that follows a periodic driving element, typically a cam, a second support for a follower member, typically a rocker arm, being arranged on a further end of the tappet pushrod, said first support comprising a passage for hydraulic medium that can be routed out of the pressure piston during operation of the internal combustion engine into an interior of the tappet pushrod, and the second support comprising a passage for the hydraulic medium to the follower member, wherein a one-way valve body is arranged in the interior of the tappet pushrod and extends for free axial displacement between a complementary valve seat facing the first support and a stop for the one-way valve body, typically a disc, facing the second support, which stop comprises at least one through-opening such that, when the one-way valve body comes to bear against the stop, a choked flow of hydraulic medium takes place toward the second support.