How to make a infinite SMOOTH scrolling background?

You might want to try changing your approach.

you can increase the framerate or decrease the scrollSpeed.  that's it.

but you'll achieve better performance by enabling the cacheAsBitmap property of BGround1 and BGround2:

var BGround1:Background=new Background(); var BGround2:Background= Background(); BGround1.cacheAsBitmap=true; BGround2.cacheAsBitmap=true; stage.addChild(BGround1); stage.addChild(BGround2); addEventListener(Event.ENTER_FRAME, moveScroll, false, 0, true); function moveScroll(e:Event): void                     {                               BGround1.x -= scrollSpeed;                                 BGround2.x -= scrollSpeed;                          if(BGround1.x <= -BGround1.width)                               {                             BGround1.x =BGround2.x + BGround2.width;                         }                               else if(BGround2.x <= -BGround2.width)                               {                             BGround2.x = BGround1.x + BGround1.width;                               }                     }