The 9 'successive extinctions', are the 8 extinctions reached through the 8 absorptions (jhāna, q.v.) and the extinction of feeling and perception' (s. nirodha-samāpatti), as it is said in A. IX, 31 and D. 33:
"In him who has entered the 1st absorption, the sensuous perceptions (kāma-saññā) are extinguished.
Having entered the 2nd absorption, thought-conception and discursive thinking (vitakkavicāra, q.v.) are extinguished.
Having entered the 3rd absorption, rapture (pīti, q.v.) is extinguished.
Having entered the 4th absorption, in-and-out breathing (assāsa-passāsa, q.v.) are extinguished.
Having entered the sphere of boundless space (ākāsānañcāyatana), the corporeality perceptions (rūpa-saññā) are extinguished.
Having entered the sphere of boundless consciousness (viññānañcāyatana), the perception of the sphere of boundless space is extinguished.
Having entered the sphere of nothingness (ākiñcaññāyatana), the perception of the sphere of boundless consciousness is extinguished.
Having entered the sphere of neither-perception-nor-non-perception (neva-saññā-nāsaññāyatana) the perception of the sphere of nothingness is extinguished.
Having entered the extinction of perception and feeling (saññāvedayitanirodha) perception and feeling are extinguished."
For further details, s. jhāna, nirodha-samāpatti.