This　paper　studies　the　stabilization　of　nonlinear　time-delay　systems　under　flexible　delayed　impulsive　control.　Some　sufficient　conditions　are　provided　for　establishing　stability　prop-erty　in　terms　of　exponential　Lyapunov-Razumikhin　functions.　It　is　shown　that　the　size　of　delay　in　continuous　dynamics　can　be　flexible.　Specially,　it　can　be　smaller　or　larger　than　the　impulsive　intervals,　and　there　is　no　magnitude　relationship　between　the　delay　in　contin-uous　flow　and　impulsive　delay.　In　most　existing　results,　from　the　impulsive　control　point　of　view,　the　Lyapunov　functions　were　based　on　the　assumption　that　there　was　a　common　threshold　at　every　impulse　point.　In　this　study,　utilizing　the　proposed　method　of　average　impulsive　estimation　(AIE),　the　rate　coefficients　are　flexible,　and　the　impulsive　delay　can　be　integrated　to　guarantee　the　effect　of　stabilization　of　impulses.　As　an　application,　the　theoretical　results　are　applied　to　the　synchronization　of　a　chaotic　neural　network,　and　the　impulsive　control　input　is　formalized　in　terms　of　linear　matrix　inequalities　(LMIs).　The　ef-ficiency　of　the　derived　results　is　illustrated　by　two　numerical　examples.(c)　2022　Elsevier　Inc.　All　rights　reserved.