I looked at messaging plug-ins for Osclass but there is nothing similar to competition like the one at o l. X.
They all stand out and are for instant messaging not private messaging like in forums for instance.
It may be just that I haven’t found or misinterpreted the way they work.
Do you know which or if exists something like that.
It’s major purpose it’s for use in the site using a smartphone.

Instant messenger & online chat are both for private communication

Thanks,
you probably guess I understand that and what happened wast that I probably didn't explain myself properly.

Something similar to what the competition is using, as I mentioned in my previous post, is what I'm looking for.

Can you be of help ?

Not sure what comoetition would be using.

The purpose would be to have some internal communication system between registered users, it could even be like pm in forums.

Both above mentioned plugins provides this, but you get to user as contact point for listing.
You cannot browse trough users those are online or available and contact them. That sounds to me like completely useless feature, easy to be misused for spam purpose.
..but maybe in future there will be plugin for that

Both are indeed 2 perfect private messengers .... So i am using them both and it is private messaging from one user to another.. For myself the problem is they do no work simultaneously in the same way but choose one and it works.....If you want your users to chat choose  chat plugin....Or private is instant messenger plugin. A live chat box is not available i think for now but it takes a lot off traffic .....Instant messenger settings is like live one on one

Thank for your replies and help.
Instant Messenger Plugin is in fact the closest to what I'm looking for.
It allows private messaging, works from inside Osclass in the user account and a simple integration, and looks like useable from a mobile phone

I would recommend instant messenger until you have real need for chat features