Counting Crows Lawsuit -- Ex-Managers Sue ... We Want Our Money!!

Counting Crows just got sued for cutting off payment to their former managers who've been pulling salaries for doing nothing for the past 13 years -- and what's really weird is ... the band agreed to that deal.

According to court docs filed last week ... Martin Kirkup & Steven Jensen of Direct Management Group repped the band from 1992 until 2001 when the Crows decided to drop them. Only problem -- DMG says it has an ironclad contract guaranteeing they continue to get paid a percentage of the band's gross earnings ... FOREVER.

The Crows got tired of that deal and stopped paying DMG in November 2013, and according to the suit ... the band is demanding a new agreement to lower payments to their ex-managers.

'Round here ... that doesn't fly with DMG. The firm is suing for the last 8 months of back pay, and wants the court to back 'em up on the whole we get paid forever thing.