In the present paper, we investigate generalized quasi Einstein manifolds satisfying some special curvature conditions $R\cdot S=0$, $R\cdot S=L_SQ(g,S)$, $C\cdot S=0$, $\tilde C\cdot S=0$, $\tilde W\cdot S=0$ and $W_2\cdot S=0$ where $R$, $S$, $C$, $\tilde C$, $\tilde W$ and $W_2$ respectively denote the Riemannian curvature tensor, Ricci tensor, conformal curvature tensor, concircular curvature tensor, quasi conformal curvature tensor and $W_2$-curvature tensor. Later, we find some suffcient conditions for a generalized quasi Einstein manifold to be a quasi Einstein manifold and we show the existence of a nearly quasi Einstein manifolds, by constructing a non trivial example.