In 1899, the All Cubans became the first all-Hispanic team to travel to the United States and stage exhibition games, against established Negro league powerhouse teams. The All Cubans kept traveling to the United States each year until 1905. Beginning in 1907, they were replaced by the Cuban Stars, which became accepted as an independent Negro baseball team. In 1916, the team was struck by controversies and competition regarding booking, which led to the creation of a new Cuban Stars carrying the same name. To differentiate between the two teams, the newer of the two was referred to as the Cuban Stars (East), which was owned by Alex Pompez and competed in the New York city area. The older team (which was owned by Abel Linares and Tinti Molina and previously had competed in the New York area) moved to the midwestern region and became known as the Cuban Stars (West).
About 1930, both Cuban Stars teams folded, but in 1935 Pompez was able to re-create a Cuban team under the new name New York Cubans. In 1935 and 1936, the New York Cubans called historic Hinchliffe Stadium in Paterson, New Jersey home. Unlike what the team's name may lead some to believe, the team was not composed exclusively of Cuban players, there were players from other Hispanic nationalities and the United States as well. In 1941, Perucho Cepeda, father of National Baseball Hall of Famer Orlando Peruchin Cepeda and a legendary player around the Caribbean himself, became the first Puerto Rican to play for the New York Cubans. Apart from Cepeda, there were also players from Mexico and the Dominican Republic playing for the New York Cubans. From 1941 to 1944, the Cubans had the services of well-known Dominican utility player Tetelo Vargas.
Only one other team of the era, the Indianapolis Clowns, boasted a line-up with as many international players as the Cubans did.