Good for you for checking your tubers.
If it were me, I would take the fuzzy tubers, rinse them off and drop them in 10% bleach/water solution, I usually let mine soak for 10 minutes or so. If any have started to go bad, you can cut that part off, tho you can't cut off where the eyes are. Let them dry, dip/roll in powdered sulphur and re-wrap-individually- in plastic wrap.
It does sounds like the root cellar is too damp. This year I also put the individually wrapped tubers in a zip lock bag, a double precaution AND I only put one variety in each bag. This was for my convenience but it doesn't hurt to be doubly cautious

It doesn't take long for rot to set in. When each tuber is in it's very own tight little cocoon of plastic wrap, if one rots, it's neighbor will be safe(er) than if they are touching bare-naked.

Thanks ladies! Seems I was on the right track. Funny how common sense does not lead a person very far astray, even if they know nothing of the particular subject. I will check on them the next time I am at my parents', and pick up some vermiculite. Thanks again.

Went to the parents' place last night. I brought my can of Lysol and gave the tubers a good douse. I only have one tuber from WHEELS (the one everybody wants!) so I HAVE to make sure it survives the winter. Moonlight Sonata I got a few from but not quite enough for everybody who wants one. They were being stored in the root cellar which seemed too damp but now they are in the entrance area to the crawl space (up off the floor) and the temp is between 45 and 50. I hope it is not too terribly warm. No sign of any growth yet though so that is good. (then again no sign of eyes either; not as good.) Time will tell I suppose.

Hi. I just received some agapanthus divisions by mail, and the tops of some of the divisions have mold on them. Can I use the 10% bleach method on them to kill the mold before I plant them. This is my first year trying agapanthus and any suggestions would be GREATLY appreciated!

I also found four large boxes of tubers slightly mushy and covered with fuzz...wil try the 10% bleach solution on half and the Lysol on the other half...wish me luck

Most of the problems related in these posts are caused by trying to store tubers that have not been properly dried before being put into storage. Air drying for a few days works quite well. One commercial grower uses a box fan to dry them. Caution: We are talking about growers who dig in wet conditions, not growers in a dry climate. But erring on too dry is better than too wet.