This　article　addresses　the　exponential　stability　problem　of　switched　systems　with　hybrid　delayed　impulses　that　depend　on　both　current　states　and　historical　states.　Some　sufficient　conditions　for　exponential　stability　based　on　Lyapunov　functions　are　obtained.　In　particular,　the　potential　stabilizing　and　destabilizing　effects　of　time　delays　in　impulses　are　investigated.　It　is　shown　that　when　continuous　dynamics　are　stable,　the　primal　stabilizing　impulses　may　destabilize　the　system　if　there　exist　delays　in　the　impulses.　Interestingly,　under　certain　conditions,　such　delayed　impulses　cannot　destroy　the　stability　of　the　whole　system　for　all　impulsive　time　sequences　with　arbitrarily　bounded　impulsive　intervals,　and　the　sizes　of　the　delays　in　the　impulses　can　theoretically　be　arbitrarily　finite.　Finally,　to　illustrate　the　validity　of　the　derived　results,　some　examples　and　simulations　are　provided.　©　2022　John　Wiley　&　Sons　Ltd.