Is there a computation class describing FOR-programs, what are the limitations? I've written an unpublished paper that describes FOR-programs.

FOR-programs are programs that only contain bounded for loops and basic operations (assignment, addition, multiplication, etc.). A bounded for loop is a for loop with a bound on the number of times that it can loop. This bound is fixed before entering the for loop for the first time and is not changed until the loop completes. 

Is there a complexity class that captures this type of programs? Since the number of for loops in a program is known in advance, the time complexity is of course limited to $O(n^k)$ with $k$ nested for loops. Thus, all FOR-programs run in polynomial time. Are there additional limitations to this class of programs?
Having just asked a very similar question:

The language of for programs can express exactly the primitive recursive functions -- see Meyer, A.R., Ritchie, D.M. (1967), The complexity of loop programs, Proc. of the ACM National Meetings, 465.  (I found a copy online here.)

The complexity class for the p.r. functions is called PR.