Virginia and Florida are suing the Bank of New York Mellon over the institution's handling of both states' pension funds.
The Virginia lawsuit filed Thursday seeks $120 million in damages. It also seeks $811.6 million in civil penalties.
Florida also is seeking damages and civil penalties.
The Bank of New York Mellon holds about $54 billion in funds for the Virginia Retirement System. Florida's system is worth some $120 billion.
Both lawsuits accuse the bank of overcharging those pension funds on foreign currency transactions.
The bank said in a statement that the lawsuits are unwarranted, and that the defendants will fight the claims in court.