The airline saw its first international service in the 1970s, when services were inaugurated to cities in Jamaica,Colombia, and Costa Rica.
The airline had stiff competition from Air Panama, until then a better known airline to the international public, until the early 1980s, but then, Copa stepped up the competition a notch, buying their first jet, a Boeing 737, and inaugurating flights to Luis Munoz Marin International Airport in San Juan, Puerto Rico, as well as to the Dominican Republic and Miami. The Boeing 737 became a staple of the Copa fleet: It is currently the only type of airliner the airline uses.
Expansion continued during the 1990s, when Copa's 737s began to be sighted at Ministro Pistarini International Airport in Buenos Aires, Argentina, Arturo Merino Benitez International Airport in Santiago, Chile, Jose Marti International Airport in Havana, Cuba, Jorge Chavez International Airport in Lima, Peru, Benito Juarez International Airport in Mexico City, Mexico and many other Latin American airports. The airline reached further internationalization by becoming, alongside TACA, Lacsa, Aviateca and Nica a member of an ambitious Central American airline group under the name of Grupo TACA. Each airline continued to operate under their own names.
In 1998, Copa reached an agreement to form an alliance with Continental Airlines. Copa's fleet nowadays reflects this alliance: Their plane's liveries resembles that of Continental's planes.
In 2000, Copa inaugurated services to Los Angeles, Orlando, as well as to Brazil.
The airline continues expanding in 2003: It inaugurated a flight to JFK International Airport in New York, and announced, in August of that year, a strategic deal with Mexico's Mexicana de Aviacion.