Allan Teo submitted the above two images of a pair of Collared Kingfisher (Todiramphus chloris) coming together and gently grabbing each other's beak.
According to Marzluff & Angell (2005), the mutual mouthing between two birds is known as allobilling. This often escalate into sharp jabs and brief fighting. This is commonly seen in ravens and less common in crows.
The question now is, are the kingfishers allobilling? Unfortunately Allan is not able to provide information on what actually happened before and after the birds started mouthing each other.
Herring Gulls (Larus argentatus) indulge in bill-touching, but this happens when the female is trying to coax the male to regurgitate food. And this is not allobilling. Again, the mutual transfer of food is not allobilling.
So, is the image captured by Chan Yoke Meng of a pair of White-crested Laughingthrush (Garrulax leucolophus) as seen below, allobilling? Maybe. Maybe not. Or are the birds indulging in allopreening? Obviously more observations need to be done on this phenomenon. Birders are urged to make detailed observations when birds touch bills and report back. Only then can we slowly understand this seldom reported phenomenon outside ravens and crows. And I am not sure whether anyone has actually reported this happening with the local crows.
Marzluff, J. M. & Angell, T. (2005). In the company of crows and ravens. New Haven & London: Yale University Press. (p166)
Input by YC, images of kingfishers by Allan Teo and laughingthrush by Chan Yoke Meng.