How long should the clean up process take? MY bosses Mac seems to be cleaning up daly for close to two hours

I had similar issues with my Time Machine drive. In addition to long cleaning or preparing times it would click a lot, i.e. heads being engaged and disengaged. I ended up erasing the drive and starting over from scratch. Haven't had a problem since.

I could do the start over from scratch because all of the files on the drives being backed up were current and there were none that I though I had deleted and might want to go back to restore at a later date.

May be an indication that your External Hard Disk is in trouble. About how old is it?

By "cleanup" are you referring to last stage of the Time Machine backup process? If so, as it appears in your post, then this would depend on a number of things.

Are these backups being done to a Time Capsule, a network drive, or to an externally attached drive? For the latter, what connection type is used between the drive and the iMac? What is the make & model of this drive?