In the mean time I've figured out what I did wrong. As signals, the stations need to be placed at the right hand side of the track depending on the train driving direction.
So yes, the stations weren't on opposite sides of the track. Fixed, and all is running fine now ...
Well, the title says it all, I try to run a single track train between point A and point B. Manually it's no problem, but on automatic it drives to one station, but for the way back all the time it says No Path? And yes, the train has locomotives at both ends. How is this supposed to work? All ...