The stability problem of switched delay systems with all subsystems unstable is investigated in this paper. A sufficient criterion is firstly proposed to guarantee asymptomatic stability of nonlinear switched delay systemswith all subsystems unstable, where the stabilization property of switching behaviors is exploited to compensate thedivergence of states. Then by constructing multiple discretized Lyapunov-Krasovskii functionals, stability criteriaare developed for linear switched time-invariant and time-varying delay systems with all subsystems unstable. Finally, two examples are provided to illustrate the feasibility, superiority and application of the proposed approach.