One of the tasks is the overdue task for today, the other is the next instance. Complete the overdue task and leave the next instance.

You could also look into "Sleeper tags" as a way to hide tasks in smart lists until a certain time before the due date:
http://blog.rememberthemilk.com/2009/04/tips-tricks-tuesday-using-sleeper-tags

As rajjan mentioned, it sounds like these are 2 instances from the same series: one is overdue and the other is the next occurrence in the series. You should be able to complete only the overdue task without affecting the next occurrence.

Hope that helps!

OK, I'm going to try that, I found that some of the duplicates were marked as postponed, so I 'completed' those. I'm sure that I've caused the problem. Perhaps I am still using something incorrectly. What I'm trying to do is use repeating tasks to remind me to do tasks on a repeating basis, but I do not want the individual 'completions' to show-up in my completed tasks list since they are relatively unimportant in terms of what I've accomplished. I would like a way to select all the completed repeating tasks in group so I can delete them (and I will click on continue repeating) - now I feel like I am faced with individually selecting tasks to delete and run the risk of deleting something I didn't mean to include. Any advice?

One of the best ways to isolate a group of tasks and make sure you're not deleting anything by accident is to use the search operators to display only the tasks you're interested in.

For example, if you had a repeating task called "Exercise" and you wanted to find all the overdue occurrences so you could delete them, the following search would locate them:
exercise AND dueBefore:tomorrow

Hope that helps!