Are you talking about conversations that would be visible to all your members, or a more private system where only the two members talking to each other can see the messages? Do you want the messages to persist, a la Facebook, or "disappear" after the conversation is over?
There are a number of ways to do this, from forum software to chat software.
private system where only the two members talking to each other can see the messages ..what ll be the cost to apply this on my website ..
You could use the PM (private message) function of open source forum software for that, such as phpBB or SMF. A PM is like an email, in that it is written in one time period and read in another, and is kept on the server until deleted by the recipient.
There are chat systems available that messaging in real time, both open source and paid. Chat is sometimes restricted on shared servers, and options exist to save the chat sessions or discard them. I haven't used any of these, so I can't recommend any (I use a commercial version of IPBoard chat for a forum I host).
Wordpress 'Buddypress Plugin' can provide such functions as well. Dolphin script is another you can look into. About cost, it's FREE to install it if you know how.
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