(23)This Regulation should allow Member States to authorise the non-commercial movement into their territory of pet animals of the species listed in Part A of Annex I accompanied by an identification document issued in a territory or a third country which applies rules the content and effect of which are the same as those applied by Member States. It should also allow Member States to authorise the non-commercial movement into their territory after a movement to a territory or a third country of those pet animals accompanied by an identification document issued in a Member State provided that the conditions to return from those territories or third countries are met before the pet animal left the Union.