Hybrid state-owned enterprises (SOEs) are listed commercial enterprises jointly owned by government and private sector entities. Public-private hybrid SOEs are prone to tension and conflict between the public and private owners who often have different goals. Different shares of public and private ownership, combined with the authority some patterns of ownership give to managers, can result in behavior and performance differences across hybrid SOEs. The major justification for using public-private hybrids derives from the evidence that the presence of private-sector shareholders improves productivity (and often profitability), relative to fully state-owned enterprises. On the other hand, the presence of multiple owners with conflicting goals could offset this benefit. To understand the trade-offs and consequences, we consider five different configurations of private and public owners, which we analyze using both property rights (PR) theory and principal-agent (PA) theory. We analyze the expected behavioral consequences by dichotomizing public ownership into either high or low public ownership and private ownership into either concentrated or dispersed private ownership, resulting in four common ownership patterns. We discuss a fifth situation where managers will dominate. We conclude that public-private hybrids are subject to significant principal-principal and principal-agent challenges as well as property rights uncertainties. However, the empirical evidence shows that these challenges are offset in some circumstances and institutional environments by the fact that private ownership does have a positive impact on productivity (and profitability) performance.