Kyutoryu is an addition to Zoro's main Santoryu. They are extensions of his spirit and part-illusion based and Kyutoryu effectively triples Zoro's potential as a swordsman and enabled him to shatter Kaku'smost powerful Rankyaku. The techniques are accessed when Zoro uses Asura, creating the initial 9-sword illusion needed to access the others. Very little is currently known about the exact nature of this brand of style as it was only so far been seen used against Kaku,Indigo, and a Pacifista.
Kiki Kyutoryu: Asura (鬼気 九刀流 阿修羅,Kiki Kyūtōryū: Ashura?, literally meaning "Demon Spirit Nine Sword Style: Asura"): The technique that allows him to use Kyutoryu. After being relentlessly attacked (and hearing Kaku insult Robin in the anime), Zoro's anger and frustration manifested itself in a dark aura emanating from himself into a being with six arms and three heads known as an Asura. In the anime, the full activation of this technique actually caused the ground to darken several meters in diameter from where Zoro stood and blow away a gust of wind from Kaku's attack. The first time he transformed was an inadvertent semi-transformation due to his agitation and only manifests as a dark aura with six arms being the only definable feature, but when he transformed a second time, he had full control over it and is shown as it is now. This is first seen being used against Kaku. This attack is powerful enough to easily disperse Kaku's Rankyaku Amanedachi and counter attack with a finishing blow, though its true nature has yet to be determined. "Ashura" is the Japanese pronunciation for Asura. This is called Demon Aura Nine-Sword Style Asura in the Funimation dub and sub and Demon Aura Nine Sword Style: Asura in the Viz Manga.
Asura: Ichibugin (阿修羅弌霧銀,Ashura: Ichibugin?, literally meaning "Asura: One Mist Silver"): Zoro's first technique with this style, holding the swords so the blades are pointing towards the victim, Zoro leaps towards them, powerfully slashing them with all nine of his swords at once afterwards ending in a position where all the swords are held in a way to make them look like they are fanning out. This is first seen being used to finish off Kaku. In the Wii video games, the "Unlimited" series, and Gigant Battle, this move does not charge against the opponent, but is like an expanding shockwave from Zoro's nine swords that slashes the opponent. In the Viz Manga and FUNimation dub, this is called Asura: Silver Mist, and in the English dub of the game Unlimited Cruise, this is called Asura Ichibugin.
Asura: Makyusen (阿修羅魔九閃,Ashura: Makyūsen?, literally meaning "Asura: Demon Nine Flashes"): Zoro approaches his target and slashes them up using all nine swords and ends with a stance where all nine swords are in a wheel shape with his Kyutoryu a few metres away from the opponent, the wound is similar in shape to the sword stance, it is similar to Brook's signature attack in that the actual effect is not seen until a few seconds later. This is first seen being used against PX-4. In the anime and in the game One Piece: Unlimited Cruise, the move has a rotating effect, but it is not certain in the manga (it seems that he charges against his opponent like with "Asura: Ichibugin". This is called Asura's Nine Lightning Slashes in the FUNimation subs.
Asura: Ugui (掘削フォース Ashura: Ugui, literally meaning "Asura: Drilling Force) Zoro uses this by activating Kyutoryu and rushing his opponent, slashing through them while holding his swords at different angles. This was first used to defeat Indigo.