A mathematical model is identifiable if and only if there is a unique relationship between each parameter value and the input-output behavior of the model. If a model is not identifiable, there is no unique solution to the parameter estimation problem, regardless of the number and types of experiments that are performed. A new method for testing the identifiability of linear time-invariant (LTI) differential-algebraic systems is presented. This method is an extension of the Markov parameter method, proposed by Grewal and Glover (IEEE Trans. Autom. Control 1976, 21, 833) and Vajda (Sci. Pap. Inst. Tech. Cybernetics Tech. Univ. Wroclaw 1985, 29, 228) for LTI ordinary differential equation systems. In the proposed method, the differential-algebraic system is partitioned into an ordinary differential equation subsystem and an algebraic subsystem. This allows for the computation of structural invariants called the generalized Markov parameters (GMPs). A system is identifiable if and only if the dependence of the GMPs on the parameters is one-to-one almost everywhere on the allowable parameter set. Tests for global and local identifiability are developed. The application of this method is demonstrated using two examples including an idealized gas-phase reactor.