Cda
Dominicana de Aviacion was the only "national" carrier in that it was the flag carrier and the only one owned by the government. It was a real airline until the mid 1980s, with routes to San Juan, Miami, Caracas and New York. It officially went bust in the mid-1990s, but had operated as a wet-lease carrier only for many years before that. The 1991 World Aviation Directly listed Dominicana as having 3 airplanes and 2000 employees. Not too shocking, then, that it went bankrupt.
In 1970, Dominicana suffered back-to-back disasters, including a new DC-9 that fell out of the sky due to contaminated fuel. The DR's only world champion boxer, and most of the Puerto Rican volleyball team, were killed.
Some personal history with Dominicana: They left me standed once after two of their jets were seized for lease non-payment in New York and Miami; and it is the only airline where an employee ever solicited a bribe from me for a boarding pass. Ah, Dominicana is truly missed!
The 1960s and 70s saw Quisqueyana airlines. It was the last airline in the world to fly the Lockheed Constellation.
Since the demise of Dominicana, the DR lost its category I status by the FAA, meaning essentially that it could not certify passenger aircraft for travel to/from the USA due to its unsatisfactory oversight of safety and security. As a result, various schemes popped up to take advantage of the DRs slot rights through wet-leases. This essentially means a DR company becomes the ticketing agent for aircraft owned and operated by foreign companies. This type of operation is notoriously unreliable and many ticketed passengers ended up getting screwed. These wet lease operations included APA, Quisqueya (different from Quisqueyana), Air Santo Domingo, Aeromar and Alas Dominicanas. The latter used a wet-leased 757 from a Turkish airline until it crashed into the Atlantic off of Puerto Plata. The crash occured after the pilot decided not to wait for the replacement of a faulty air speed indicator.
Also, some foreign airlines created Dominican marketing subsidiaries in the early 2000s, also to take advantage of slots while using foreign aircraft and crews. These included Lan Dominicana (Chile) and Aerocontinente Dominicana (Ecuador).