New type of vector singularities inherent in partially coherent combined beams is explored. There are the polarization degree singularities, such as U (unpolarized) and P (completely polarized) elements of a field. The fundamental properties of such singularities are derived for the general case of elliptical polarization basis using the notion of the complex degree of polarization represented at the Stokes space that is limited by the Poincare sphere. Experimental procedure for detecting the polarization degree singularities and reconstruction of a vector skeleton of partially coherent combined beams is presented.© (2009) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.