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In this paper, a class of two-step continuity Runge-Kutta(TSCRK) methods for solving singular delay differential equations(DDEs) is presented. Analysis of numerical stability of this methods is given. We consider the two distinct cases: (i)τ≥ h, (ii)τ< h, where the delay τ and step size h of the two-step continuity Runge-Kutta methods are both constant.The absolute stability regions of some methods are plotted and numerical examples show the efficiency of the method.