Macross Plus

Three decades after the great war between the humans and the Zentradi, the U.N. government is developing new technologies to use in their transforming fighter aircraft. Two great pilots, the loose cannon Isamu Alva Dyson and the Zentradi half-breed Guld Goa Bowman, are selected to each test a new aircraft (Shinsei Industries' YF-19 "Alpha One" & General Galaxy's YF-21 "Omega One") for Project Super Nova, to choose the newest successor to the traditional Valkyrie fighter. Their own personal grudges end up disrupting the tests and wreak havok on the program. (Wikipedia)