  In this paper, we will investigate the geodesic mappings of some special
Riemannian manifolds. First, we will prove that if there exists an Einstein
tensor preserving geodesic mapping from a quasi Einstein manifold $V_{n}$ onto
a Riemannian manifold $\bar{V}_{n}$, then $\bar{V}_{n}$ is nearly quasi
Einstein. Furthermore, we will obtain new results concerning the geodesic
mappings of Ricci recurrent and Ricci symmetric manifolds. Next, by using these
results, we will investigate the geodesic mappings of pseudo Ricci symmetric
and almost pseudo Ricci symmetric manifolds.
