The aim of this paper is to give oscillation criteria for the third-order neutral dynamic equations with distributed deviating arguments of the form $$ \Big[r(t)\big([x(t)+p(t)x\tau(t))]^{\Delta\Delta}\big)^\gamma\Big]^\Delta+\int^d_cf(t,x[\phi(t,\xi)])\Delta\xi=0, $$ where $\gamma>0$ is the quotient of odd positive integers with $r(t)$ and $p(t)$ real-valued rd-continuous positive functions defined on $\Bbb T$. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.