The Cryptic Corporation is a team of people managing The Residents. Whereas a single band might be okay with only one manager or none at all, The Residents have kept themselves anonymous for almost 40 years. Gotta give them respect for that. Their anonymity is based on the theory of obscurity (saying that artists will produce their best works when the expectations or influences of outside world are not there to bind them) by (the possibly fictitious) N. Senada. This is why they need a few guys to do about all non-musical work for them.
Those people would be Homer Flynn and Hardy Fox, the directors of the organization. Along with being managers, they also speak for the band. As for being managers, they also managed Ralph Records from 1976 to 1986. In the beginning (around 1976) there were four members, the mentioned Flynn and Fox but also Jay Clem and John Kennedy, who left in 1982. They have all denied being The Residents. This is very debatable, however, as the information provided by The Cryptic Corporation sometimes sounds like it was picked up from a fantasy book, for example Snakefinger picking N. Senada up in Bavaria, while on his way to America from Great Britain.
William Poundstone presents a theory in his book Big Secrets, that Flynn and Fox are the most likely the leading Residents: in interviews, fans have also noted that Flynn's voice has very much in common with the singing Resident. According to the Cryptic Corporation, Flynn, among others, does the visual artwork. The artwork is done under a name that, when spelled, will become "Pornographics", such as Pore No Graphix or Pore-Know Graphics. Fox is the so-called sound engineer, producing, engineering, mastering and so on their music.