<p>Systems of differential-algebraic equations, not necessarily regular, with unknown inputs in dynamic as well as in measurement equations are studied. Causality of the systems is analyzed, and strict causal detectability conditions are established. Further, necessary and sufficient conditions for the existence of Luenberger observers have been derived in terms of original system coefficient matrices. The process to obtain these conditions is based on numerically stable orthogonal transformations. Design methodology for a reduced order observer is elaborated. Simulation results for the proposed observer are presented with a physical example.</p>