Partially coherent scalar sources with cylindrical symmetry radiating outwards are introduced. Homogeneous cross-spectral densities are shown to possess angularly modulated Hankel modes, whose amplitudes are subject to a filtering process during propagation. Simple criteria for treating such sources are given. For the case of an incoherent cylinder, the number of effective modes is found and spatial coherence is shown to appear in the radiated light. The radial coherence of the radiated field is then examined. Non-homogeneous cylindrical sources are also introduced.