The chain stumbles over the gears on the back cassette.
I have a set of Campagnolo gears back and forth and a no-name chain.
I can only use one of 10 gear rings on the back cassette (Veloce).

Is the problem, that the chain have to be Campagnolo compatible ?

First things first...Is it a new chain? A new cassette? Chains wear out and no longer glide cleanly over the cogs of the cassette. Often, by the time you notice that happening, you have also worn out your cassette and need to replace it, as well.

Terms? By stumble do you mean that the chain won't stay fully engaged with a rear cog and the chain climbs up, over and retries to settle into/engage the cog's teeth with any forceful pedaling? So no attempt to be shifting and the chain stays on the same cog. Or do mean that during shifting the chain can't engage any (but one) of the cogs?

Chains really want to be cog count (10 speed in this case) compatible with the cog set. Chains can develop tight links that mimic worn chain skipping. Chains can develop twisted or otherwise damaged links (often during forceful shifting).

Cog sets need to have the correct cog to cog spacing for their cog count, misplaced spacers is not uncommon. The last smallest cog can sometimes be installed off rotational index causing the chain to not like that cog.

Too many possibilities for the minimal data given. Andy

Can you wrap the chain around any of the middle sprockets on the rear stack and have it seat itself fully? If not, it's definitely not the chain for that group. If it does, then that doesn't necessary eliminate the chain as the problem. It needs a certain amount of clearance to keep itself seated between them when moving. I don't know how much.

What did you change? An incorrect adjustment can cause this as well as a dozen other things.

@Papa Tom
The cassette is a not much used 10 speed Campagnolo Veloce.

@Andrew R Stewart
Yes. By stumble I mean that the chain won't stay fully engaged with a rear cog and the chain climbs up, over and retries to settle into/engage the cog's teeth with any forceful pedaling.

I found out that the chain is a new SRAM PC 830.
When I shift gears while the wheel is lifted from the ground, it works fine.
When I ride, I can only use one of the middle rear gears with no chain climbing.

I've tried with an old Campagnolo derailleur and with a new Shimano 105, the result is same.

So what are you doing running an 8 speed chain on a 10 speed cassette?

(Hint - that's the problem)

Thank you all.
I'll go shopping a new chain

Agreed that the 8s chain won't work well at all with a 10s cassette, so I'd fix that first.

Unless you're using friction shifters, which isn't likely considering that you have a 10s cassette, a 105 derailleur isn't going to shift well paired with a Campy cassette. Depending on how "old" the campy derailleur is, it may not handle a 10s cassette either. Still, your odds improve dramatically using a Campy derailleur.

I don't recall seeing which brake/shifters you are using - again, you will have much better shifting if you run all Campy. The 11s cassettes are pretty much interchangeable between Campy and Shimano, but 10s was not.

I think SRAM would be rightly upset at being called "no name".
They got into the chain business when they bought Sachs/Sedisport.

I've just ordered a SRAM PC1031
... and sorry [MENTION=199407]sram[/MENTION]

Know that you will also have to size the chain to your bike. You typically don't just connect the ends together and use the full length of what you bought. You have to remove some links or else your shifting will again be poor or won't even go to the smaller gears on the rear.

There are different procedures for different mfrs and setups. On a typical 2x front you can loop the chain around the largest front and largest rear sprocket without going through the rear DR cage and then count two more links and split the chain there.

@Iride01
Google & YouTube are my best friends

For me too - and I always read the comments on YouTube videos to see if there's a mistake in the process. And for any how-to, I make sure I watch as many videos as possible to see if the general process seems right.