Conway v. Stannard was a United States Supreme Court case that addressed the issue of whether a state court had the authority to grant a new trial in a case that had already been decided by a federal court. The case involved a dispute between two parties over a contract for the sale of a steamboat. The plaintiff, Conway, had sued the defendant, Stannard, in a federal court in Louisiana. The federal court had found in favor of Conway and awarded him damages. Stannard then appealed the decision to the Louisiana Supreme Court, which granted him a new trial. The Supreme Court held that the Louisiana Supreme Court did not have the authority to grant a new trial in a case that had already been decided by a federal court. The Court reasoned that the federal court had exclusive jurisdiction over the case and that the state court could not interfere with the federal court's decision. The Court also noted that the state court's decision was in direct conflict with the federal court's decision and that the state court had no authority to grant a new trial. The Court's decision in Conway v. Stannard established the principle that state courts do not have the authority to grant a new trial in a case that has already been decided by a federal court. This principle has been applied in numerous cases since then and has been an important part of the American legal system.

In Conway v. Stannard, the Supreme Court was asked to decide whether a state court had jurisdiction over an action brought by a non-resident against another non-resident in which the cause of action arose out of events that occurred within the state's borders. The majority opinion held that it did not have such jurisdiction and reversed the judgment of the lower court. Justice Field dissented from this decision, arguing that under general principles of comity between states, courts should be allowed to exercise their authority when both parties are citizens or residents outside its boundaries but where one party has committed some act within its borders giving rise to a claim for relief. He argued further that if states were denied this power then they would be unable to protect their own citizens who may suffer injury while visiting other jurisdictions and thus would be deprived of an important right without due process as guaranteed by Article IV Section 2 Clause 1 (the Full Faith and Credit clause) of the Constitution.