basil seedlings dying from the top

The leaves on my basil seedlings are shrivelling and drying up. I'm suspecting some kind of fungus but really can't determine if that's it. I had been putting them outside to harden off but have since stopped doing that once I saw what was happening. The stems seem to be ok, so I'm not suspecting damping-off disease. However it's not all of them.The bigger ones seem to be doing ok. I'd appreciate any help.
Thank you,
Sal

It sounds like they might have gotten sunburned if it is just the tops. Were they in a lot of sun when you put them out side?

Tigerlily, I hope you're right. Yes I did put them out in the sun but I didn't think it was that strong. And whatever this is, it's now spreading to other seedlings, like peppers, zinnias, lupine and tomatoes. The odd thing is that I've been putting them outside for at least 2 weeks now and they didn't show any of these signs until a few days ago. Some of my citrus seedlings are also being affected. Those however, I've noticed stem rot. Not top damage. So maybe you're right on. I'm going to bring them inside for a few days to see if they revive. At least thase that still have some leaves on them.
Thanks tigerlily,

Sal