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My sons are coming from JFK to Rome via Brussels, arriving at 7:45 am on Friday Aug 25 on Brussels Airlines. Then, they're flying on Ryanair to Rome, departing at 10:10 am.

They will need to claim and re-check their luggage. Is this going to be enough time?

Hard to say. If all goes well, it's certainly enough time, but there isn't a lot of room for error, delays, or hiccups.

Ryan air has a strict 40 min deadline for bag drop. So they need to be at the bag drop at 9.30 at the latest. 9.00 would be better since you still need to go through security to get to the gate.

Security at Brussels is very strict after the bombings last year.

On arrival, your sons will have to collect their bags and then go through customs and immigration at Brussels. How long that takes, depends often on time of day and also nationality.

If you have status with the transatlantic airlines (or buy some priority package), they will often unload your bags first, which can be a big time safer. Not only do you get your bags quickly, you are also at the top of of queue for passport control.

There's always the possibility of a delay. However,

I have traveled from Abu Dhabi to Brussels, collected my bags, went to deposit my bags for Ryan Air to London more than 40min in advance, with plenty of time left to get a beer: my layover was 2:05.

So barring any delays, they have more time than I had. Let us know how it works out!