Yes, you must carry both passports.

Expired passport is TIMATIC conform.

With water damage, data page and visa need to be readable though.

Backup Post: I have a ten year visa that expires next year, but it is in a passport which was damaged and subsequently cancelled after it went through a washing machine. I know that the visa would still be valid if the passport was just expired and renewed, but is it still valid if the passport was cancelled due to damage?

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First, I'm assuming you're a US citizen, because it's different if you're Canadian (and I don't know anywhere else that does 10 years).

Second, if the passport is stamped as cancelled, there might be issues.

Many years ago, I had a passport stolen with a Chinese visa in it. I had reported the passport stolen (to the US Passport Agency) and gotten a new passport, but before I contacted the Chinese consulate, the police recovered my backpack (it was about a month later).

I used my new passport with my old Chinese visa for another 3 or so years before the visa finally expired. So not exactly the same situation, but not that far off.

If your Chinese visa is damaged, there's a chance they will have an issue, but as long as it's not torn and completely readable, I would be comfortable using it.