Abstract: In  this  paper,the  asymptotic  behavior  of ordinary  differential  equations   is    studied.Set    stability,set   uniform    stability,set   unstability,set  asymptotic       stability,set       globally       asymptotic       stability,set        qusicontractive  stability,set   globally   qusicontractive    stability,set   contractive    stability  and  set  globally  contractive  stability,are  consldered  some  theorems  for  all kinds of stability mentioned-above are proved by means of the Lyapuovlike      functions.