Velikanova became a dissident in 1968. That year she witnessed the 1968 Red Square demonstration, an open protest by seven people against the crushing of the Prague Spring reforms by the Soviet-led invasion of Czechoslovakia. She had gone to the Square with one of the demonstrators, her husband Konstantin Babitsky, so as to testify as a witness in court if needed. Like the other protestors Babitsky was arrested on the spot. He was sentenced to three years in exile in the Far Northern Komi Region. Velikanova's experience at the trial where her testimony was distorted and used against Babitsky, led her to decide she would never again participate in such judicial proceedings. (Nor did she, see below, when she was herself put on trial in 1980.)