Damiano David -- the lead singer of Maneskin, which took top honors at the singing competition -- could be seen at one point during the broadcast in what looked to many like a compromising position. In the now-viral video of the bizarre moment, you see him leaning down face-first toward the table in front of him, hovering for a bit ... and surfacing again.

There's a giant bowl blocking the camera from seeing what's right below in that shot -- but many saw it as it happened live Saturday, and immediately thought he was doing drugs.

Yeah, at first glance ... it does look like he might be doing a line. But, then again, it's hard to tell what the hell's actually going on down there. Some have also noted there are no visible signs of drug residue as he comes back up -- namely, white powder ... aka, cocaine.

The European Broadcasting Union -- which organizes the Eurovision show -- has said it's aware of the video, and that they're looking into the matter with an investigation of their own. Apparently, they tried getting an on-the-spot drug test done for David right then and there, but weren't able to get it together in time before the band flew out for the night.

However, David and his bandmates say they're more than willing to submit to voluntary drug tests ASAP ... as they insist there was zero drug usage by the singer or anyone else nearby.