Oncest is the fandom given name to the relationship between two Once-lers, although the term can be altered when referring to a certain combination of Once-lers involved. It is one of the most popular ships in the Once-ler fandom.
The pairing emerged from the prospect of a universe where the Once-ler, before he became big and rich from selling Thneeds, meets his future green suited "greedy" self (also dubbed as Greed-ler by the fandom). This pairing now is referred to as "Classic Oncest" due to the many alterations that the term "Oncest" has suffered.
The relationship does not necessarily need to be sexual to fit in the term; granted it is a recurring case in Fanfiction and artwork, Oncest can refer to a platonic relationship between two Once-lers.
There are many types of Oncest involving fandom created ask-blogs, and the name has evolved over time to depending on the people involved. Usually the adaptation is a fusion of the names from the Once-lers participating in the relationship. (i.e. Ask-Swag-Onceler x One-ler : Swoncest; Bitter Once-ler x Young Entrepreneur: Bittre).
This ship is far from canon, which the fandom is aware. In many cases the shippers of this pairing are called mentally unstable and/or "in need of psychiatric evaluation" because of the mere strangeness of it to outsiders. While inside the fandom it is quite normal and may be even abnormal not to ship this in one way or another.
There also be classic Oncest, which be the young Once-ler who be wearing grey on top of and makin out with his older self in green. While not as popular as it used to be, it is still well loved by the fandom.