Watari Shirow, 60 years old, is the director of TERRA, Ayato's and Itsuki's biological father, and was also Dr. Rikudoh's assistant before he was the director of Terra. During the time when Maya was under the care of Rikudoh, Shirow and Maya got romantically involed and eventually got married. Shirow's original name was actually Kamina Shirow (that's how Maya got the Kamina last name), but due to Maya being branded a traitor, he was forced to change his name to Watari Shirow to avoid any charges of dealing with the Mu and being branded a traitor himself.
Shirow is always busy in trips. Before he was always working with Rikudoh in the Neirya ruins, and as a director he's even busier with the politics of the organization. So he's not around all the time in the series. In fact, it was during one of his excursions when he was still together with Maya and Ayato that Ayato decided to tag along with him and there he met Haruka (the scene at the very end of the series). Much of Shirow's character is shrowded in mystery but a few things are obvious. He loves to joke around, so even though he may have a troubled soul inside, he always makes his best to keep everybody in high spirits. Another characteristic of Shirow is that even though he's not outspoken about it, he feels special fatherly feelings for Itsuki and Ayato. On a few occasions Ayato and Shirow clashed in arguments, but he always tried to keep his cool and advice the young boy. His relationship with Itsuki is a bit more mysterious as not much is shown, the only thing we know is that everytime these are together they don't speak very much. At the end of the series we see Shirow on his knees in grief when he sees Itsuki's and Nanomori's bodies.
Dr. Rikudoh, 62, is the uncle of Haruka and Megumi, Maya's adoptive father, and also a renowned archeologist. Dr. Rikudoh is the person, other than Bahbem, that knows the most about the origin of the Mu and the RahXephon since he's the one that researches and uncovers the truth. Futagami (the reporter) often tries to get information out of Rikudoh but fails everytime. We often see that Rikudoh's personality is easy going and may even appear to be care free. He loves playing shogi (Japanese chess), and his mastery of the game is almost as impressive as his ability to avoid Futagami's questions, nobody can really beat him in shogi except Quon. He's also the first person to make Ayato feel like he's at home when he gives him the name tag to put in front of the house.
Though Rikudoh holds such big secrets and is one of the most important characters in the story, he actually finds time to take care of his family, he was particularly attached to Maya. He often refers to Maya as his "Moon Princess", a character of Japanese folklore that came from the moon only to be taken away when she has matured enough. Which is exactly what happens after Maya decides to create Tokyo Jupiter and leave the world behind. Even after this, he still loves Maya as a daughter, and Maya respectively loves him as a father. We can see that Maya even paid her respects at the end of the series before the tuning. Years after Maya left, Haruka moved in with her little sister Megumi to Rikudoh's place. At the end of the series, Rikudoh decides to stay close to Megumi and protect her, meanwhile Haruka goes on to pursue Ayato.
Watari, Rikudoh and Kunugi have very close ties as friends. After Kunugi was kicked out of the military it was Shirow that got Kunugi to work for Terra and fight againts the Mu.