This　paper　concerns　that　a　non-weighted　l(2)/L-2-gain　performance　for　asynchronously　switched　systems　can　be　achieved　in　both　discrete-time　and　continuous-time　cases.　Based　on　the　constructed　Lyapunov-like　functions　with　average　dwell　time　(ADT)　method　and　inequality　analysis　technique,　a　non-weighted　l(2)/L-2-gain　for　asynchronously　switched　nonlinear　systems　can　be　guaranteed,　which　improves　the　existing　results.　Meanwhile,　for　asynchronously　switched　linear　systems,　the　piecewise　Lyapunov　matrices　are　constructed　and　linear　matrix　inequalities　(LMIs)　conditions　are　derived　to　attain　a　non-weighted　l(2)/L-2-gain　performance.　Finally,　some　examples　are　provided　to　illustrate　the　theoretical　results.　(C)　2021　Elsevier　Ltd.　All　rights　reserved.