A Riemannian space \(V_ n\) is said to admit an almost geodesic mapping of type \(\pi_ 2\) onto \(\bar V_ n\) (N. S. Sinyukov), if there exist tensor fields \(\phi_ i,\psi_ i,\sigma_ i,\nu_ i\) and \(U^ k_ i\) satisfying the conditions: \({\bar\Gamma }{}^ h_{ij}=\Gamma^ k_{ij}+\phi_{(i}\delta^ k_{j)}+\psi_{(i}U^ k_{j)}\), \(U^ k_{(i,j)}+\psi_{(i}U^ n_{j)}U^ h_ r= \delta_{(i}\delta^ k_{j)}+\nu_{(i}U^ k_{j)}\), where the notations are chosen in the usual manner. This mapping is said to be reduced (V. S. Sobchuk), if the following relations are satisfied \(U^ r_ iU^ h_ r=\epsilon\delta^ h_ i\); \(\epsilon =\pm 1\); \(\psi_{i,j}=U_{ij}+\psi_{(i}U^ r_{j)}\phi_ r\), where \(\phi_ i=\phi_{,i},\psi_ i=\psi_{,i}\) and \(U_{ij}=g_{ir}U^ r_ j\). The author proves the following theorem: Let \(V_ n (n>2)\) admit a reduced almost geodesic mapping onto a semisymmetric Riemannian space \(\bar V_ n\). Suppose, moreover, that the function a-\(n\epsilon\) does not vanish identically, where \(a=a_{ij}g^{ij}\) and \(a_{ij}=\phi_{i,j}-\phi_ i\phi_ j-\phi_ rU^ r_{(i}\psi_{j)}+\epsilon\psi_ i\psi_ j\), then \(\bar V_ n\) is of constant curvature and \(V_ n\) is locally symmetric. This theorem generalizes results of V. S. Sobchuk when \(V_ n\) is locally symmetric.