 For Kramer vs. Kramer , Streep won both the Academy Award and Golden Globe Award for Best Supporting Actress . She was also awarded the Los Angeles Film Critics Association Award for Best Supporting Actress , National Board of Review Award for Best Supporting Actress and National Society of Film Critics Award for Best Supporting Actress for her collective work in her three film releases of 1979 . Both The Deer Hunter and Kramer vs. Kramer were major commercial successes and were the consecutive winners of the Academy Award for Best Picture . 
