The U.S. federal court system hears cases involving litigants from two or more states, violations of federal laws, treaties, and the Constitution, admiralty, bankruptcy, and related issues. In practice, about 80 % of the cases are civil and 20 % criminal. The civil cases often involve civil rights, patents, and Social Security while the criminal cases involve tax fraud, robbery, counterfeiting, and drug crimes. The trial courts are U.S. district courts, followed by United States courts of appeals and then the Supreme Court of the United States. The judicial system, whether state or federal, begins with a court of first instance, whose work may be reviewed by an appellate court, and then ends at the court of last resort, which may review the work of the lower courts.

What are the two federal courts under the supreme court? Let's have some stream of consciousness first.
The relevant information to answer the above question is: The trial courts are U.S. district courts, followed by United States courts of appeals and then the Supreme Court of the United States. So, the answer is The trial courts are U.S. district courts , followed by United States courts of appeals.