They in turn had then received the green light from their respective governments.
"Would they then debate the differences between their respective governments?"
The project is still being studied by the respective governments.
The two decided to refer the entire matter back to their respective governments.
I don't care how highly placed in your respective governments you are.
"We shall report back to our respective governments and let them decide what to do."
We can do it without the consent of their respective governments.
In the end the two agreed to refer the matter to their respective governments.
Both projects are still being promoted by their respective national governments.
The judges were not free to act independently of their respective governments.