I have to disagree with ShreevatsaR. His suggestion is incorrect. Let's break things down. Here it is in its original form:
Besides the managers, Pete, John and Eric, also the secretary, Mary, came along to the meeting.
Now, let's simplify this to the basics. Let's get rid of the lists of people and of a few extraneous words—also and along.
Besides the managers, the secretary came to the meeting.
Now, let's begin to add the folks back in. At this point, it should be clear that the people are appearing parenthetically. When you insert a parenthetical item into a sentence, you offset it with commas. This is a simple trick I use to explain to people who are struggling with comma usage how to use them or where to put them.
Mary is parenthetical, so we add her back in, set off with commas:
Besides the managers, the secretary, Mary, came to the meeting.
The managers are also parenthetical, so let's add them back in, too, set off with commas, of course:
Besides the managers, Pete, John, and Eric, the secretary, Mary, came to the meeting.
This is correct. If you don't like the way it reads, then you should just rewrite it. Let me throw out a couple ideas:
Not only Pete, John, and Eric (managers) came to the meeting, but also Mary (secretary).
Both managers (Pete, John, and Eric) and the secretary (Mary) came to the meeting.
I'm not saying these are better (or even all that good!), only that you might consider some alternatives if you don't like the original.