Hall & Oates are on the outs over what songs John Oates is allowed to sing by himself ... sources familiar with the dispute tell TMZ.

As we reported, Daryl Hall got a restraining order against his longtime compadre last week, although the file has been sealed and no information is publicly available.

The 2 -- BTW, the most successful duo in music history -- have been in arbitration, we're told, trying to work out the ground rules of who can sing what as a solo artist, along with money issues of course ... so say our sources.

Hall ran to court on November 16, asking for a restraining order against Oates ... and the judge granted that order the next day.

It's no coincidence ... Oates had a slew of concerts scheduled for this month -- November 1, 3, 4, 6, 9, and 10. The November 9 and 10 concerts were postponed until next year, although no reason was given. This aligns with Hall going to court just days later for the restraining order.

Hall appeared on Bill Maher's "Club Random" podcast last year and made it clear ... something bad was going on in the group. Bill asked about his "partner" John Oates, and Hall fired back Oates was not his partner creatively ... they were just business partners.  Translation ... them's my songs, not his.

As for what songs are on the table, well, there are a lot, including, "Kiss On My List," "Rich Girl," "Maneater," "You Make My Dreams," "One on One," "Out of Touch," "You've Lost that Lovin' Feeling," and "Private Eyes."