madrid airport connection to barcelona

Same question that is always asked in this case: Is this one booking or two?

If one booking, the airline would not have taken the booking if they didn't think it was possible, and if you miss the second flight because the first was late, it is their problem to get you to Barcelona on a later flight.

If two bookings - you need to be lucky. You will need to collect your bags, exit through arrivals and then check in again (hand over your bags) for the second flight.
Where are you flying from? Intercontinental flights can easily be 1 hour late landing.
Immigration can take 1 hour+
What is the minimum check-in time for your second flight?
How lucky do you feel?

That is a decent amount of time to make that but it depends on the flight into Madrid arriving on time. If you miss it they will put you the next one with space available

Which terminals?... Madrid's airport is a large airport... it has five of them.

Which terminals?... Madrid's airport is a large airport... it has five of them.

American Airlines uses Terminal 4 & 4s (Satellite). I've flown on AA & arrived at the satellite terminal (flight was an hour late). It was a long walk to the 4s train station, then a short ride to terminal 4, then another long walk to immigration & baggage pickup. The airport web site says Veuling uses Terminal 4.
I don't know how generous Vueling is if you miss a flight. As Chris F says, if you bought the Veuling tickets separately from the AA tickets, they could become worthless or subject to additional charges if you miss the flight, depending on the terms of the specific tickets you bought.

Thanks for all your help.