Riemannian spaces $\overset{*}{K}{}_n^s$

The algebraic classification of Riemannian spaces of $s$-recurrent curvature ($R_{ijkl,m1\,m2\dots ms}=\Omega_{m1\,m2\dots ms}R_{ijkl}$) is given. The structure of the curvature tensor and the Ricci tensor of such spaces is elucidated. It is schown that the theorems of A. Lichnerowicz, W. Roter and A. Thompson are true also for the 2-recurrent spaces of arbitrary signature.