This thesis contributes to the qualitative theory of differential-algebraic equations(DAEs) by providing new stability criteria for solutions of a class of nonlinear, fully implicit DAEs with a properly stated derivative term and tractability index one and two. A generalization of the Andronov-Witt Theorem addressing orbital stability is proved. To this purpose, a state space representation of differential-algebraic systems based on the tractability index is developed which has advantageous properties, e.g. moderate smoothness requirements, commutativity with linearization and an autonomous structure in case of autonomous DAEs. It allows a suitable definition of characteristic multipliers referring to the inherent dynamics, but given in terms of the DAE. Furthermore, the fundamentals of Lyapunov's direct method with respect to diffe- rential-algebraic systems are worked out. Novel denitions of Lyapunov functions for differentiable solution components of a DAE are stated, where the monotoni- cally decreasing total time derivative of a Lyapunov function along DAE solutions is expressed in terms of the original system. The topology of the domain of the inherent dynamics turns out to be decisive for nonlocal existence of solutions given a Lyapunov function. As a result, practical stability criteria for bounded solutions of autonomous DAEs and for general solutions of DAEs with bounded partial derivatives of the constitutive function arise. Known contractivity denitions for DAEs can be interpreted in the context of this approach
