Alicia Vikander and Michael Fassbender: Awards Season's Most Elusive Couple

Now You See Them, Now You Don't: Alicia Vikander and Michael Fassbender Are This Awards Season's Most Elusive Couple

Throughout their two-year relationship, the two have shied away from the spotlight, rarely stepping out together

And the award for Hollywood’s most private couple goes to …

Alicia Vikander and Michael Fassbender might be two of Hollywood’s biggest stars, but the ultra-private couple prefer to keep a low profile.

The two started dating after meeting on set of their 2014 film The Light Between Oceans, but throughout their two-year relationship they’ve shied away from the spotlight, rarely stepping out together.

While their low-key status has caused their relationship to be plagued with breakup rumors over the years, Vikander, 27, and Fassbender, 38, put any doubts to rest when they made their awards-show debut as a couple at the Golden Globes in January.

Although they sat next to each other inside the ceremony, they did their best to keep the attention off their relationship, walking separately on the red carpet and dodging questions about their romance. But before taking their seats inside, the actor bashfully admitted that he was “very proud” of his girlfriend’s impressive year.

Later in the night, the couple were even spotted holding hands as they left an afterparty at West Hollywood’s Sunset Tower Hotel.

The Danish Girl actress and the Steve Jobs star had a similar routine at the BAFTA awards on Feb. 14, walking the carpet alone but sitting happily next to each other once inside. The two were even spotted celebrating their respective BAFTA nominations at one of London’s posh spots the night before.

But just as the two appeared to be getting more comfortable in the limelight, they also seemed far from interested in showing some PDA – notably when an audience kiss cam tried to nudge them to share their first public smooch at the BAFTAs.

The couple refused to kiss as the cam hovered over them for several seconds.

“Michael Fassbender having none of it,” wrote one Twitter user, who grabbed a screenshot of the moment.

If the couple’s routine is any indication, fans are no doubt betting that come Oscar time, Vikander and Fassbender will walk the carpet separately – but sit together inside for the show.

Watch our Live from the Oscars Red Carpet show on PEOPLE.com starting at 5:30 ET/2:30 PT on Feb. 28 – and the 88th Academy Awards at 7 ET/4 PT on ABC. Click here for a handy ballot of this year s Oscar nominees!