Main conflict within NATO was between the European countries, on the one side, and Turkey (a NATO, but not yet an EU member state), on the other. Ankara was, for some time, against military intervention in Libya, and used the platform of NATO to voice its opinion. Eventually, however, Turkey approved NATO's engagement in Libya probably in large part because the Arab League has been a surprisingly vocal supporter of the military enforcement of the no-fly zone.
Another major diplomatic scandal in the West had less to do with NATO taking over command of the allied activities in Libya than with France's initial unilateral decision to intervene militarily in Libya, without consulting Germany. The German government was unhappy about this turn of events, and voiced its disapproval. On the other hand, Germany made it clear that it was willing to support the coalition indirectly, even before NATO's decision to take over the operation.
This point of view was expressed by Andreas Umland in his article "Libya: it is a different situation" originally published on ValdaiClub.com
Another major diplomatic scandal in the West had less to do with NATO taking over command of the allied activities in Libya than with France's initial unilateral decision to intervene militarily in Libya, without consulting Germany. The German government was unhappy about this turn of events, and voiced its disapproval. On the other hand, Germany made it clear that it was willing to support the coalition indirectly, even before NATO's decision to take over the operation.
This point of view was expressed by Andreas Umland in his article "Libya: it is a different situation" originally published on ValdaiClub.com