I would have thought that "Hjorten var LIGE ved at løbe, da det så bilen" would be closer to the English sentence "The deer was ABOUT to run.....".
The Danish "Hjorten var ved at løbe...." would surely be "The deer was running...."
"Hjorten var lige ved at løbe, da den så bilen"="The deer was just about to run when it saw the car".
"The deer was running...."="Hjorten løb...".
Thanks for all of your comments tddk. They are very helpful. A Happy New Year to you.
Er det også rigtigt : ... når den så bilen. ?