I just bought a 2001 or so Lemond Poprad. The rear derailleur is bent. It is a Shimano Sora. The cassette has eight gears. What inexpensive derailleur can I use as a replacement. Thanks.

shimano Tiagra or 105.

Mountain Equipment Co-op is like REI in the US. They carry a number of 8 speed derailleurs.
Altus M310 is $35 CDN
Claris RD 2400 is $42 CDN.

It would be easier to get them in the US, but those are functional. There are also a number of MB deraileurs that would work as well.

I'm sure you can find them in the US.

Is the derailleur bent, or is the hanger bent? (Or both?)

Shimano Claris RD-2400 Rear Derailleur > Components > Drivetrain > Road Rear Derailleurs | Jenson USA

brand new claris less than $25

+1 when the derailleur gets banged up it is possible/probable that the hanger is bent as well. Best to have the hanger alignment checked to avoid a lot of hair-pulling when derailleur adjustment time comes along.

I am not sure of what the hanger consists, to be foolishly honest. It seems to me, however, that the derailleur is bent, i.e. the top part that the chain is wrapped around.

These are all very helpful comments. Thank you.

The hanger is the part the RD bolts on to, have a look at the Park Tool how to site https://www.parktool.com/blog/repair-help to get an idea of what is what on a bike.

You've got a few things to take into account...

Sora is a Shimano road bike groupset, so a direct replacement would be another Shimano road bike derailleur like Sora, Claris, Tiagra, or 105. (Not 11-speed, though.) Shimano mountain bike derailleurs were compatible up through 9-speed, so you could use one of those.

You'll need to make sure the derailleur cage (length between pulleys) is long enough to handle your gear ratios. Each model typically comes in multiple versions -- e.g. short cage, medium cage, or long cage.

The derailleur may or may not be bent -- we really can't tell without pics. But if the derailleur got hit/pulled/snagged hard enough to bend it, there's a really good chance the derailleur hanger got bent, too. The hanger is the tab on the frame the derailleur screws into, and it needs to be aligned properly in order for shifting to work well. There's a shop tool specifically for checking and setting hanger alignment.

If you're trying to keep the replacement cost low, I'd look for a used 8 or 9 speed RX100, RSX, 105, or Tiagara rear derailleur on eBay or on your local Craigslist. You should be able to find some for between $10-$20, including shipping (if necessary).

If you are patient, you should also be able to find a new 8-speed Sora rear derailleurs (and front derailleurs) on eBay (try looking for Seller Crossroads), if you wait and watch for $10, or less including shipping (I usually don't bid more than $3). I've gotten a couple fronts and rears for my parts bin in the past year (I've bought a number of used 105 8 & 9 speed derailleurs to put on bikes during the same period for $1-$15). IMHO Sora is good for spare parts bins, and emergency spares, and will work fine when new, but they aren't very high quality, and Shimano budget derailleurs often don't hold up very well over the long run. Sora and Claris have stamped steel parts that will rust where RX100, RSX, Tiagara, and 105 are alloy (lighter and more rigid).

Any MTB that is below 10 speeds.

Shimano Acera or Sora (even Claris) are both good options, though for Acera it is 100% sure it can handle the chain length changes whether the bike has double, or triple crankset with a wide cassettte.

I'd recommend a LBS, but this is from Amazon:

Acera:

Amazon.com : Shimano Acera : Rear Bike Derailleurs : Sports & Outdoors


Claris:

https://www.amazon.com/gp/product/B00...UFWW7BYRY4GYW2


For explanation of chain wrap capacity and cog size ranges, RDs in general:

Rear derailleur