The United States brought an appeal against William Kohler, the claimant of The Brig Neurea. This case centered around a dispute between the two parties regarding whether or not Kohler was entitled to compensation for his vessel and cargo that were seized by U.S. authorities during the Mexican-American War in 1846. The Supreme Court found that since there had been no formal declaration of war at the time of seizure, it could not be considered as a lawful act under international law and therefore did not entitle Kohler to any compensation from the government for his losses. Furthermore, they held that even if such a declaration had been made prior to seizure, it would still have been illegal due to its violation of neutrality laws which prohibited private citizens from engaging in hostilities with foreign nations without permission from their own government first. As such, they ruled against Kohler's claim and denied him any form of reparation for his losses incurred during this incident

In The United States v. The Brig Neurea, Her Tackle, &c., William Kohler, Claimant (1856), the Supreme Court was asked to decide whether a vessel that had been seized by the government for violating revenue laws could be forfeited and sold without compensation to its owner. Justice Curtis wrote a dissenting opinion in which he argued that such an action would violate due process of law as guaranteed by the Fifth Amendment of the Constitution. He reasoned that since no criminal proceedings were brought against Kohler or his vessel, it was improper for them to suffer forfeiture without being given notice and opportunity to defend themselves in court. Furthermore, he noted that even if there had been some violation of revenue laws committed by Kohler's vessel, this did not necessarily mean it should be subject to forfeiture; instead any penalty imposed should have taken into account all relevant circumstances surrounding the case before determining what punishment was appropriate.