Singular systems (descriptor systems, differential-algebraic equations) are a recent topic of research in numerical mathematics, mechanics and control theory as well. But compared with common methods available for investigating regular systems many problems still have to be solved making also available a complete set of tools to analyze, to design and to simulate singular systems. In this contribution the aspect of stability is considered. Some new results for linear singular systems are presented based on a generalized Lyapunov matrix equation. Particularly, for mechanical systems with holonomic constraints the well-known stability theorem of Thomson and Tait is generalized.