This paper investigates the factors that hindered the accomplishment of the Arab Maghreb Union, despite the economic, political, social, and security challenges posed to its countries by globalisation. The paper focuses mainly on the reasons that held back Algerian politicians from supporting the efforts of the regional countries and the international community for putting an end to the dispute over the Western Sahara, along with acknowledging the historical rights of Morocco in it. As a way out of this gridlock, Morocco proposed a political solution through a Saharan self-rule; a move that is widely welcomed by the international community as a viable means for the economic and social development, as well as for facing anticipated future challenges.