Brooklyn Beckham and Nicola Peltz let the music take control at Coachella ... vibing with one another while artists took the stage -- and leaning in to suck a little face.

The two stars were spotted hanging out at the popular music festival in the desert on Friday ... and, they were spotted smooching up a storm -- leaving the rest of the crowd behind and enjoying their own private moment in public.

Beckham and Peltz are clearly very much in love ... putting on a united front in public -- support Brooklyn definitely needs now while he feuds with his little brother Romeo.

We broke the story ... Romeo and Brooklyn aren't speaking because of Romeo's girlfriend -- Kim Turnbull.

While Kim and Brooklyn were romantically linked a few years ago, we're told that's all water under the bridge ... but, the issue here is whether Kim is dating Romeo for the right reasons -- and, it seems Brooklyn isn't convinced.

Our sources say Brooklyn and Nicola won't even attend family functions where Kim's present -- even though Victoria and David Beckham trust Kim around Romeo.

Despite their fractured relationship, our sources insist Brooklyn isn't beefing with Romeo personally ... he just doesn't trust Kim's intentions.