I have set the settings of my LrC version such, that it saves a backup of the catalogue each time I am closing the program. Today, I have noticed by chance, that these backups occupy a substiantial amount of disk space in course of time. Do I need the old copies of the catalogue (i.e. files of the type "Lightroom Catalog.lrcat") or can I delete them ?
As stated, yes, delete all/any you desire. But keep in mind, that this is only a backup of your catalog. Not all the other important data that needs to be backed up like presets, profiles, and most importantly, your images! You might want to follow a real and robust backup schema that backs up all the data you cannot afford to lose, then turn OFF this catalog backup that isn't very effective. On Mac, there's Time Machine, but maybe better is something like SuperDuper (very inexpensive) that can back up everything, every day, (or night) automatically while you're sleeping.
Author “Color Management for Photographers" & "Photoshop CC Color Management/pluralsight"