This dissertation aims to investigate the entry decision of a Low-Cost Carrier (LCC) in a market where the incumbent firm, the Full-Cost Carrier (FCC), has a competitive advantage due to the existence of captive loyal consumers, who are only willing to fly with this company. As the LCC is more efficient than the FCC in terms of operation costs, this dissertation investigates under which conditions for cost differences and dimension of FCC’s captive segment, will the LCC entrance occur. With this goal in mind, a theoretical model of price competition is proposed and solved, using game theoretical tools. We conclude that, as expected, the entry of the LCC will be more likely in markets with a lower proportion of captive consumers to the FCC, which translates into a greater potential demand (selective market) for the LCC. The entry will also be more likely the greater the cost advantage of LCC compared to the FCC. Regarding the impact on profits, we conclude that the FCC will face greater losses if its initial competitive advantage (proportion of captive consumers) is less significant and faces the actual entry of a very efficient LCC. With regard to the LCC, we show that the entry becomes more likely the greater the lower is its cost in comparison to the incumbent company. With these results, we conclude that if the FCC wants to smooth price competition with a cost-efficient LCC, it should devote resources to increasing passenger loyalty. On the other hand, LCCs interested in entering a market should guarantee cost levels low enough to address the disadvantages of competing with a FCC with captive consumers.