She co-founded the Spanish-English ensemble Teatro Dúo/Duo Theatre with Manuel Martín Jr. and the lesbian theater Medusa's Revenge with Ana María Simo.
[2] They decided to form the theater group Teatro Joven and staged Abelardo Estorino's one-act play Los Mangos de Caín.
Shortly before the planned third performance of the piece, the Executive Bureau of the Young Communist League shut the show down.
[3] She acted in productions at INTAR, Greenwich Mews Theater, and La MaMa Experimental Theatre Club.
[7] In 1981, Alabau appeared in La MaMa's production of Jose Triano's The Night of the Assassins, directed by Endre Hules.
In the book, she reinterprets the Greek myths of Clytemnestra and Electra, transforming the context from heterosexual to lesbian.