This research is supported by a grant of NSF of China(1 96 0 1 0 1 5 ) ;the Science Foundation for distin-guished young scholars of Henan Province;also a grant awarded to him by NSF of Henan Provice (994 0 5 1 80 0 )
Project supported by the National Natural Science Foundation of China (Grant No. 19601015);the Natural Science Foundation of Henan Province
The quasitriangular structure of the twisted smash coproduct Hopf algebras is studied. Necessary and sufficient conditions for the quasitriangularity of the twisted smash coproduct Hopf algebras are obtained.