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[For the entire collection see Zbl 0699.00032.] A manifold (M,g) is said to be generalized Einstein manifold if the following condition is satisfied $$\left({\nabla }_{X}S\right)(Y,Z)=\sigma \left(X\right)g(Y,Z)+\nu \left(Y\right)g(X,Z)+\nu \left(Z\right)g(X,Y)$$ where S(X,Y) is the Ricci tensor of (M,g) and $\sigma$ (X), $\nu$ (X) are certain $\ell$-forms. In the present paper the author studies properties of conformal and geodesic mappings of generalized Einstein manifolds. He gives the local classification of generalized Einstein manifolds when g($\psi$ (X),$\psi$ (X))$\ne 0$.