iemannian manifolds where the Jacobi operator $J(X)$ has globally constant eigenvalues are said to be Osserman; there is a generalization of this condition due to Stanilov. Manifolds where the skew-symmetric curvature operator $R(\pi)$ has pointwise constant eigenvalues are said to be Ivanov-Petrova or simply IP. We generalize these concepts to the complex setting and present examples of complex Osserman and complex IP algebraic curvature tensors and metrics.