Martin Luther King Jr's concept of "militant nonviolence" was based around his belief that all civil rights protests should remain nonviolent, no matter what is happening. This idea was used numerous times in the South during the Civil Rights movement. A perfect example would be the sit-ins that took place at the Woolworth lunch counter in North Carolina. This form of peaceful protest that brought attention to injustice of segregated lunch counters resulted in several black citizens being verbally and physically harassed. Despite this, not a single member of this group retaliated.
Individuals like Malcolm X opposed this philosophy. Malcolm X believed that black citizens should use self defense if being attacked by a white citizen. He believed that for too long, blacks have been beaten up and abused by white citizens. He felt that civil rights should be achieved by any means necessary.