This case was a dispute between the City of New Orleans and the United States Ex Rel. Gaines's Administrators. The dispute arose from a contract between the City of New Orleans and the Gaines's Administrators for the construction of a levee. The City of New Orleans refused to pay the Gaines's Administrators for the work they had done, claiming that the contract was void because it had been made without the approval of the City Council. The Gaines's Administrators then brought suit against the City of New Orleans in the United States Supreme Court. The Supreme Court held that the contract was valid and enforceable. The Court found that the City Council had no authority to invalidate the contract, as it had been made with the approval of the Mayor and the Board of Public Works. The Court also held that the City of New Orleans was liable for the work done by the Gaines's Administrators, and ordered the City to pay the full amount due. In conclusion, the Supreme Court held that the contract between the City of New Orleans and the Gaines's Administrators was valid and enforceable, and that the City of New Orleans was liable for the work done by the Gaines's Administrators. The Court ordered the City to pay the full amount due.

In the case of New Orleans v. United States Ex Rel.: Gaines's Administrators, the Supreme Court was asked to decide whether a state law that prohibited African Americans from attending white schools violated the Equal Protection Clause of the Fourteenth Amendment. The majority opinion held that it did not violate this clause because states had broad authority to regulate public education and could choose which races would attend different schools if they so desired. However, Justice Harlan dissented on this ruling, arguing that such laws were unconstitutional as they denied African Americans equal protection under the law by denying them access to educational opportunities available only to whites. He argued further that these laws created an unequal system in which one race was favored over another and thus violated both due process and equal protection clauses of the Constitution.