First three images: courtship – male (at bottom of first image), hovered, waved front legs and curled abdomen in the air.

No mating occured, possibly beacuse the other fly (at top of first image) appears to be a male (I could be wrong, but it looks like it has claspers).

Next three images: passive fly at top of first photo.

Last three images: fly performing the courtship at bottom of first photo.

Flies are about 20 mm long.

I saw these flies chasing each other on a tree trunk bathed in the sunshine. It seems that they were mating in an unusual way, with the male's front legs touching the female's tail. At first I thought they were robber flies. But after checking the wing vein, I thought they must be something else, most probably something new for me.