The International Society for Krishna Consciousness draws its legitimacy from its place in a long succession of spiritual teachers and disciples (parampara). There are four major disciplic successions (sampradayas), ISKCON belongs to the Brahma Sampradaya, founded by Lord Krishna Himself.
There are many branches to this sampradaya. Our society belongs to the branch founded by Sri Caitanya Mahaprabhu in the 16th century.
The principle is that Vaisnava teachings should be passed on, unchanged, from guru to disciple. The most prominent devotees in this lineage are accepted as acaryas: those who teach by example, who carry the line forward. Listed below are the acaryas s, starting from Lord Krishna Himself all the way down to the Founder Acharya of ISKCON Srila Prabhupada:
1) Krsna, 2) Brahma, 3) Narada; 4) Vyasa, 5) Madhva, 6) Padmanabha, 7) Nrhari, 8) Madhava, 9) Aksobhya, 10) Jaya Tirtha, 11) Jnanasindhu, 12) Dayanidhi, 13) Vidyanidhi, 14) Rajendra, 15) Jayadharma, 16) Purusottama, 17) Brahmanya Tirtha, 18) Vyasa Tirtha, 19) Laksmipati, 20) Madhavendra Puri, 21) Isvara Puri, (Nityananda, Advaita), 22) Lord Caitanya, 23) Rupa, (Svarupa, Sanatana), 24) Raghunatha, Jiva, 25) Krsnadasa, 26) Narottama, 27) Visvanatha, 28) (Baladeva) Jagannatha, 29) Bhaktivinoda, 30) Gaurakisora, 31) Bhaktisiddhanta Sarasvati, 32) His Divine Grace A. C. Bhaktivedanta Swami Prabhupada.