This could be an issue. I would inform Google.
Also as I understood from other post here on WW, if one of your accounts get banned then second could also get banned as "related".

I've been logging in from same computer to both accounts for years with no problem.

First, ask google, regardless of the answers you get here. It may be fine for one person, and cause lots of problems with another.

Myself, I've checked up to three accounts from the same PC. One that is mine personally, one that is a corporation's, and one that's my mom's. Never had a problem.

You may or may not have problems opening a second account if it has your name on it. You probably don't want it to be solely in your brother's either. You can form a corporation with three people. Now if only one of you are married, you could meet the three person rule, but can run into problems later (for example, you and your wife can overrule just your brother, or vice-versa). So hopefully both of you are married and all four can start the corporation, or perhaps you can talk one of your parents into it (just make sure the parent likes you the best :) ). It's a bit more paperwork, but if you ever have problems down the line...well the corporation is just like a person. It can own the site, and if you have let's say legal problems, the corporation gets sued for everything it owns (which would be limited to just the site or other business related stuff, none of your personal possessions). Also it makes signing up for Adsense a snap, the corporation is it's own entity, so no problems if you AND your brother had individual accounts already.

I don't know about C-corporations but in my state an S-corporation can be started and run by as few as one individual (me in my case).

I have two corporations each with its own Adsense account. Since a corporation is a legal entity, two accounts is very legit and above board in terms of complying with Adsense's TOS. I didn't try to hide anything from Adsense. The address and contact information for both accounts is the same.

I use the same computer to log into both accounts, typically one immediately after the other. I have for over two years.

I have noticed when I get my monthly checks that that "client ID" is the same on both checks even though they have different account numbers. So clearly Adsense knows of the relationship between the accounts. There isn't a question in my mind that if one account got banned that they would probably ban the other account too.

Guys? The OP is in Italy. US-centric legal advice is unlikely to be useful to him :(

I would think that a corporation is a legal entity in pretty much any country.

yes, but 'c-corporation' 's-corporation' - no idea what they are. Very US-centric.
The OP was asking if he is going to have a problem logging into multiple accounts from the one IP, not how to form a corporation in the US :)

True, but he did mention he was setting it up with someone else, and I figured it'd be nice to address that as well. Had I noticed he was from Italy (I generally don't check people's profiles before responding to a thread, sorry), I wouldn't have even bothered going into that.

Fair enough :)
Being elsewhere myself, I feel as if I have tripped while walking whenever I come across a thread which answers with a US-specific answer to a generic question. I had to say something :)

It's okay to do, as far as Google is concerned, as long as you first ask permission. You must email support and explain why you need two accounts, and await for them to reply.

Thanks for all the replies. It is actually a LLC and has already been set up and is, coincidentally, in the US.

But as leadegroot said, my question was more towards the adsense side of things, the LLC already having been set up. I think I'll just contact G about this. If we set up the biz account and put my brother's name and address in the contact info, then I go logging in, that might cause some issues.