Bill Cosby once said (well, in a standup so probably lots of times) that you're not really a parent till you have 2 - until then you don't deal with the "stop touching me" and "mine!" and "mommy, he...." *grin* It's kinda part of the whole parenting deal, especially when they're so close in age. My point here is that it is completely normal.
My stragegy at 2 and 3 was to prevent and separate. The consequences are still a bit fuzzy, especially for the 2 year old. He my be able to say he is in timeout for pushing, whatever, but it is hard for kids this age to see ahead and think "I was in time out last time I did this, I shouldn't do it so that I don't get timeout again". Try to have enough toys for them to share (very popular ones may need duplicates), and sometimes playing separately, in different areas or even different rooms, is necessary. When they do fight, its best to separate them and remove the item in contention (if there was one) from both. Just say something like "I can see you need to be away from each other for now." The big thing is to stay calm and do your best to be fair (I've seen some kids who "fight" just to get mom upset, and some who are very sneaky about getting their sibling in trouble). When they do play nicely, make a comment like "I'm happy to see you playing together, it looks like you're having fun." But don't make a HUGE deal, either - if it feels too over-the-top, they won't believe you.
And give it time. Siblings are always going to have some points of not getting along. But as they get older the relationship changes and things can be very different. My boys (7 and 9) are best friends most of the time, but can fight like nothing else at others (down to hitting!) And my brother and I were constant rivals as kids but now we're best friends as adults. As your kids get older, their relationship will adjust, and you can teach them more about being kind to siblings.