I have bought a pack of sliced beef and opened it up as soon as I got home. Judging by the date on a package, it was packed on the same day I bought it. It was red on the outside, but dark and brown-ish where individual peaces touched each other.
When meat is first cut, it is purplish in color. If it is exposed to enough oxygen, it can turn a bright red. Eventually it will turn brown.
If the meat is cut and exposed to air, but then deprived of enough oxygen to turn red, the color will go from purplish directly to brownish. (See this USDA FAQ, which was also quoted in the answer to a similar question here on ground beef.)
Also, many meat packers make use of small amounts of carbon monoxide during the packaging process. Exposing fresh meat to carbon monoxide will retain the bright red color on the exterior for a longer period.
In the past, the interior browning with exterior redness was mostly visible in heavily processed meat (like ground beef), where the grinding exposes a lot of meat surface to air, but then deprives it of oxygen. I assume that the carbon monoxide processing now makes it possible to see meats with less cutting involved (like sliced meats or steaks) where the exterior stays red for much longer, even as the cuts that are stacked or overlap may sometimes turn brown on the surface.
It's fairly common for beef to turn a little brown in places due to oxidation - myoglobin, which is what makes meat red (and is what people often mistake for blood in a rare steak) oxidises to form metmyoglobin, which is brown.
If you followed good storage practices (it hasn't been out at room temperature for more than 2 hours), and it has no odd odour or sliminess, you should be fine. Exercise your own judgement though - if in doubt, throw it out!