A new class of partially coherent light sources is introduced. At the source plane, they exhibit perfect coherence along any annulus that is concentric to the source center. Between two points at different distances from the center, coherence can be partial or even vanishing. Such sources can be synthesized by using a generalized form of van Cittert-Zernike theorem where axial sources are used. Beams radiated by this type of source are analyzed at the source plane and upon free propagation for some simple cases.