Living in a Big Way (1947) is an American musical comedy film starring Gene Kelly and Marie McDonald as a couple who marry during World War II after only knowing each other a short time.
 This was director Gregory La Cava's final film.
Symphony of Six Million is a 1932 American Pre-Code film directed by Gregory La Cava and starring Ricardo Cortez, Irene Dunne and Gregory Ratoff.
 Based on the story "Night Bell" by Fannie Hurst, the movie concerns the rise of a Jewish physician from humble roots to the top of his profession and the social costs of losing his connection with his community, his family and with the craft of healing.
Gallant Lady is a 1934 American Pre-Code drama film directed by Gregory La Cava and written by Sam Mintz.
 The film stars Ann Harding, Clive Brook, Otto Kruger, Tullio Carminati, Dickie Moore, Janet Beecher and Betty Lawford.
 The film was released on January 5, 1934, by United Artists.
Gregory La Cava (March 10, 1892 – March 1, 1952) was an American film director best known for his films of the 1930s, including "My Man Godfrey" and "Stage Door", which earned him nominations for Academy Award for Best Director.
The Gay Defender is a lost 1927 American silent drama film directed by Gregory La Cava and written by Ray Harris, Grover Jones, Herman J. Mankiewicz, George Marion Jr., Sam Mintz and Kenneth Raisbeck.
 The film stars Richard Dix, Thelma Todd, Fred Kohler, Jerry Mandy, Robert Brower, Harry Holden and Fred Esmelton.
 The film was released on December 10, 1927, by Paramount Pictures.
Tell It to Sweeney is a 1927 American comedy silent film directed by Gregory La Cava and written by Monte Brice, Kerry Clarke, George Marion Jr. and Percy Heath.
 The film stars Chester Conklin, George Bancroft, Jack Luden, Doris Hill, Frank Bond and William H. Tooker.
 The film was released on September 24, 1927, by Paramount Pictures.
Yesterday Girl (German: Abschied von gestern, "Farewell to Yesterday") is a 1966 New German Cinema film directed and written by Alexander Kluge.
 The film is based on the short story "Anita G." (1962), which is also by Alexander Kluge.
 The film tells the story of Anita G., a young East German migrant to West Germany and her struggle to adjust to her new life.
Alexander Kluge (born 14 February 1932) is a German author, philosopher, academic and film director.
The La Cava Bible or Codex Cavensis (Cava de' Tirreni, Biblioteca statale del Monumento Nazionale Badia di Cava, Ms. memb.
 I) is a 9th-century Latin illuminated Bible, which was produced in Spain, probably in the Kingdom of Asturias during the reign of Alfonso II.
 The manuscript preserved at the abbey of La Trinità della Cava, near Cava de' Tirreni, contains 330 vellum folios which measure 320 by 260 mm.
My Man Godfrey is a 1936 American screwball comedy film directed by Gregory La Cava.
 The screenplay was written by Morrie Ryskind, with uncredited contributions by La Cava, based on "1101 Park Avenue", a short novel by Eric Hatch.
 The story concerns a socialite who hires a derelict to be her family's butler, only to fall in love with him.
 The film stars William Powell and Carole Lombard.
 Powell and Lombard had been briefly married years earlier.

Question: Were Alexander Kluge and Gregory La Cava both film directors? 
Answer: yes