thanks for all your reply. but now my xbees are in 1. router AT mode 2. co coordinator AT.
Next if i use two usb adapter it works good that is “TWO WAY COMMUNICATION”. so i think both xbees are proper. but still i am not able to succeed in two way communication.
i dont know of hardware hand shaking thinks can you help me in this ?
Most likely not. But you should not that most Arduino code wants the radios in API mode. What I would suggest is removing the XBee module from the Arduino and then connecting the XBee socket to the PC and a Terminal Emulator so you can see what is coming out. By doing this, you will be able to verify if you are using the proper port in your code and what you expect to come out to the radio is what you think it is.
i have not experimented with xbee in API mode. So far what i have tried has made me to come to a conclusion that its not possible for 2 way chat communication using xbee and arduino on both sides.
No that is not entirely correct. Yes, API mode is the preferred method and the rout that all of the available libraries have taken. So unless you want to write the connection entirely from scratch and without any lib files, you need to use API mode.