it's not dh I have the issue with, intact he is a bit 
like me!
We both share a laptop at the moment so if we are having a nosey on Facebook there is a good chance it may be the other ones page that is still logged in (just clearing this up that there is no snooping involved)
Brief history is we did not speak to bil for many years (dh younger bro) we made contact a few months ago and there is a new girlfriend on the scene.
I am not shy in admitting my dh is the nicer, kinder, better looking and more successful of the two brothers (his brother is a lazy slob but that is a whole other thread) right from the first meeting I felt the gf was overfriendly with dh and he said after we left she was to full on for his liking. I put it down to just the way she was but now it seems to be stepping up a gear.
On a recent day out she would not leave dh's side, was getting quite awkward how she always had to be next to him or sitting beside him, now he has started receiving private Facebook messages from her. Nothing at all sinister but just friendly banter and asking how he is etc (never any mention of me or dc)
It's starting to niggle at me now, why send private messages she already replies to anything he puts on his wall so why not just put up a public post?
I'm not worried at all about anything happening between them dh finds it as odd as me but bil and her have a child together plus dh has just started talking to bil again and I don't want anything/one to cause a rift between then again.
Not sure if I should casually mention I see all her messages and hope that makes her think twice or if I am a complete loon and she is naturally just a flirt?