Active　control　is　an　effective　method　for　making　two　identical　Rossler　and　Chen　systems　be　synchronized.　However,　this　method　works　only　for　a　certain　class　of　chaotic　systems　with　known　parameters　both　in　drive　systems　and　response　systems.　Modification　based　on　Lyapunov　stability　theory　is　proposed　in　order　to　overcome　this　limitation.　An　adaptive　synchronization　controller,　which　can　make　the　states　of　two　identical　Rossler　and　Chen　systems　globally　asymptotically　synchronized　in　the　presence　of　system＇s　unknown　constant　parameters,　is　derived.　Especially,　when　some　unknown　parameters　are　positive,　we　can　make　the　controller　more　simple,　besides,　the　controller　is　independent　of　those　positive　uncertain　parameters.　At　last,　when　the　condition　that　arbitrary　unknown　parameters　in　two　systems　are　identical　constants　is　cancelled,　we　demonstrate　that　it　is　possible　to　synchronize　two　chaotic　systems.　All　results　are　proved　using　a　well-known　Lyapunov　stability　theorem.　Numerical　simulations　are　given　to　validate　the　proposed　synchronization　approach.　(C)　2002　Elsevier　Science　B.V.　All　rights　reserved.