Well i have been running azureus for quite a long time, but Iam having this NAT
problem ever since I started running this program,it may be because of my router I guess,i guess i need to do something with my router settings,can pls somebody help me pls...
If you have a router, you need to forward whatever port azureus is using to your computer. It's done via your router's setup panel, but that varies between routers.
You could post the router model you have here and someone might chime in with help, but your best bet is probably the Azureus Wiki, which has a whole section on instructions for various routers: