First, it is my understanding that there is no official hand to hand training program for SEALs. Because each team trains and functions as a separate group they are free to hire and employ experts to train with as their operational needs dictate. So each team can and does have different systems to draw upon and no one thing is "official". So it is be a mixed bag.
For example, my teacher, Paul Vunak was contracted to teach his own personal version of JKD (Progressive Fighting System's the RAT) as the "official" h2h for around four years with SEAL Team 6 in Virginia Beach (I believe it was from 87-91). He left a core of JKD inspired intructors that he certified behind when he left (Pat Bagley, Pat Tray, and Frank Cucci I believe) to carry on the JKD centered training..
Paul discussing RAT on youtube
http://www.youtube.com/watch?v=7szJl4ZLVPI
and
http://www.youtube.com/watch?v=qcVN4Xn0Dyw
Frank Cucci old vids on youtube
http://www.youtube.com/watch?v=68pNX7YkbIM
There have been other groups and systems used. SCARS by Jerry Peterson was taught at BUDs and for awhile was kinda "official". It was heavily inspired by San Soo kung fu I believe. It was better than karate I guess, but... yech...
SCARS on youtube
http://www.youtube.com/watch?v=m7xpCr7lUWE
SAFTA, (a SCARS knock-off) was taught somewhere along the line,,, I love the mustache in this youtube video and he DID train Jon Hess in UFC 5
SAFTA on Youtube
http://www.youtube.com/watch?v=17oSzGQtBxo
I know that Duane Dieter has been teaching SEALs his system for a while now. I seem to remember that his system was based off wing chun concepts, but I could be wrong.
Dieter on youtube
http://www.youtube.com/watch?v=tEHo4l0ucmY
One guy even told me they did Military style Krav Maga in his team.
As said before, no SEALs normal operational duties regularly require them to fight h2h. It is a confidence builder, warrior mentality training skill and a necessary component of survival for wtshtf. I had a ex-SEAL tell me once that he only ever had to use his h2h skill when he was being covered by a fully armed team.
p.s. Steven Seagal was only a SEAL in the movies...