WHAT is his deal...frick!?

Maybe he's not interested in having a girlfriend or acting like he does in front of other people. He may be one of those guys who need some extra prodding to get him to go in a definite direction. Tell him you've been dating for almost two months and you'd like to know where the relationship is headed. If he freaks out and disappears, you know you just saved yourself who knows how many months of only dating with no movement forward. He may just be waiting for you to show some sign that you want things to move forward. As for his behavior in front of other people, it's easier to be closer when alone for some people than it is to do out in public. He may even be trying not to come off as possessive by not doing all of that. Could be a lot of things. Just consider his personality since you've gotten to know him a bit and then sit him down for a talk.