This talk is concerned with asymptotic stability of linear neutral delay differentialalgebraic equations and Runge-Kutta methods.First,we give a new equivalent sufficient condition for the neutral delay differential-algebraic equations to be delay-independently asymptotically stable.Then we investigate the asymptotic stability of the numerical solutions generated by the Runge-Kutta methods combined with Lagrange interpolation.Some results on the asymptotic stability of Runge- Kutta methods of high order are given.Finally,numerical examples of index-1 and index-2 are conducted to confirm our numerical stability result.