De Saussure v. Gaillard was a United States Supreme Court case that dealt with the issue of whether a state court had the authority to issue a writ of error to a federal court. The case arose when the defendant, Gaillard, was convicted of a crime in a state court and appealed the conviction to the federal court. The state court then issued a writ of error to the federal court, which the federal court refused to accept. The Supreme Court ultimately held that the state court did not have the authority to issue a writ of error to a federal court. The Supreme Court reasoned that the state court was not a court of the United States, and therefore did not have the authority to issue a writ of error to a federal court. The Court further reasoned that the state court was not a court of appeals, and therefore did not have the authority to review the decision of the federal court. The Court concluded that the state court did not have the authority to issue a writ of error to the federal court, and that the conviction should stand. In conclusion, the Supreme Court held that the state court did not have the authority to issue a writ of error to the federal court, and that the conviction should stand. This decision established the precedent that state courts do not have the authority to issue a writ of error to a federal court.

In De Saussure v. Gaillard, the Supreme Court was tasked with determining whether a state court had jurisdiction over an action brought by a non-resident against another non-resident in regards to real estate located within the state's borders. The majority opinion held that such jurisdiction did exist and affirmed the decision of the lower court. However, Justice Field dissented from this ruling on two grounds: firstly, he argued that there was no basis for asserting personal jurisdiction over either party; secondly, he noted that even if such jurisdiction existed it should not be exercised due to its potential conflict with other states' laws or interests. He concluded his dissent by noting that "the power of one State to exercise judicial authority beyond its own limits is necessarily limited" and thus any assertion of extra territorial power must be done cautiously so as not to infringe upon other states' rights or interests.