The solvability and stability analyses of linear time invariant systems of delay differential-algebraic equations (DDAEs) are analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in terms of spectral conditions. Furthermore, examples are delivered to demonstrate that the eigenvalue-based approach in analyzing the exponential stability of dynamical systems is only valid for a special class of DDAEs, namely, non-advanced. Then, a new concept of weak stability is proposed and studied for DDAEs whose matrix coefficients pairwise commute.