"Rank-Up-Magic" (ＲＵＭ Rankuappumajikku) is an archetype of Spell Cards from the Yu-Gi-Oh! ZEXAL anime. Their effects allow one to Rank Up an Xyz Monster. An Xyz Monster with a Rank higher than the target is Special Summoned from the Extra Deck, and the targeted Xyz Monster and its Xyz Materials become Xyz Materials on the newly Summoned monster. This process is called "Chaos Xyz Evolution" (when performed with Barian, "Numeron", or "Argent Chaos" Force) or "Rank-Up Xyz Evolution" (when performed by "Astral" Force).
The Rank-Up Spells were first introduced in the anime by Girag, who used "Rank-Up-Magic Barian's Force" to brainwash students from Heartland in order to take the "Numbers" from Yuma, Astral and Shark. Each time it would be used to Rank-Up Xyz monsters into "CXyz" monsters in order to overpower the "Numbers".
Mizar used it next when he himself ranked up his "Number 107: Galaxy-Eyes Tachyon Dragon" in order to form it's Chaos form. This monster wasn't seen on this encounter.
Alito and Girag both ranked up their respective "Number 10X" monsters. Both of them were defeated by Yuma and Astral (Girag was also defeated by Vector posing as Ray).
Yuma gained his own Rank-Up spell in the form of "Rank-Up-Magic Limited Barian's Force" during his Duel with Girag from "Ray" but was later transformed into it's true form of "Rank-Up-Magic Numeron Force" by ZEXAL II.
Vector also demonstrated his mastery of Rank-Up Spells when he used "Rank-Up-Magic Barian's Force" on his "Number 10X" monster, but also to brainwash Brook Walker.
When Yuma went to the Astral World looking for Astral, he Dueled against Eliphas who used "Rank-Up-Magic Astral Force" in his Duel against Yuma.
Quattro, Trey and Quinton also demonstrated the ability to Rank-Up their monsters with the Spell Card "Rank-Up-Magic Argent Chaos Force" when Dueling the Barians.
When Shark became Nash once again he augmented the Barian Emperors with the Spell Card "Rank-Up-Magic - The Seventh One" which worked specifically for their "Number 10X" monsters and was used by all the Emperors save Vector.
Vector gained a new "Rank-Up-Magic" card during his Duel with Nash in Episode 137, "Rank-Up-Magic Admiration of the Thousands".
Also, Nash gained a new "Rank-Up-Magic" card in the form of "Rank-Up-Magic Quick Chaos", becoming the first Quick-Play Spell Card in that set.
Astral's final Duel against Yuma revealed he possesses three "Rank-Up-Magic" cards, "Double-Rank-Up-Magic Hope Force", "Rank-Up-Magic Dark Force" and "Hyper-Rank-Up-Magic Ultimate Force".