<p>In this paper, we consider the stability and asymptotic stability for a class of nonlinear delay differential–algebraic equations by means of linearization process. This validity is obtained by showing the equivalence between the direct linearization and the linearization of the original problem. In addition, we also study the numerical methods to solve the nonlinear problems, and apply the implicit Euler method and the backward differential formula method to solve the system, and obtain the sufficient conditions for stability and asymptotic stability. Examples show that our methods are simple and effective.</p>