Luca wrote:

I have planted a Nelly Moser about a month ago. It seemes to be
doing great until 2-3 days ago, when all the leaves on one of the two
stems started wilting.

Since this is a baby plant, it needs to be nursed along. If it has been
hot and dry where you are, you might need to water more frequently.
Nelly Moser is unfortunately susceptible to Clematis Wilt, and there is
unfortunately not much you can do if that's the case. You might want to
check into this disease to see if the description of the disease matches
what you're seeing.

Also the leaves are browning from the ground
up.

That is normal. Clematis do tend to lose some leaves towards its base
during the hot summer. Mulch heavily and do your best to keep its roots
cool.

The other stem still looks healthy. I am guessing one of the
stem got damaged, even though I cannot see anything wrong...?

It is possible that maybe the stem got damaged, as they can be a little
brittle. Once the plant is well established, it will do just fine.
Look up its culture requirements, and pamper it for a little bit. BTW,
don't be surprised if the clematis doesn't appear to be doing much of
anything for the first couple of years. They have a very extensive root
system, and normally concentrate their efforts towards that end.

Suja