An admiralty court has jurisdiction over all the incidents of the principal cause of action. In Putnam v. Lower, 236 F.2d 561 (9th Cir. Wash. 1956), the court held that when a libellant brings a maritime suit before the admiralty court, the court may dispose of it completely without the need of any other suit, or any other court. Admiralty courts have inherent authority to take security by bond, recoqnizance, or stipulation and to proceed to judgment thereon according to the course of admiralty.
An admiralty court may examine nonmaritime contracts to determine if such contracts constitute a valid defense, although the same contracts will not support a libel or cross-libel for affirmative relief. An admiralty court cannot entertain a suit to reform a release from liability executed under a mutual mistake merely because it pertains to a maritime claim. However, when such a release is pleaded in defense against assertion of that claim, admiralty is not barred from determining if it was executed by the parties under mutual mistake.[i]
[i] Swift & Co. Packers v. Compania Colombiana Del Caribe, S. A., 339 U.S. 684 (U.S. 1950)