The First and The Second banks of America (1791 - 1811, 1816 - 1836 respectively) were the only representatives of the United States Treasury (the only banking system allowed to operate on national level, i.e dealing with huge sums of hard cash) at the time. The other banks operated on state level, or on a private party level. In 1863 the U.S. Congress apparently passed an act (the first National Bank Act of 1863) that provided a system for just these nationwide "National Banks". They established a minimum sum of money each bank should hold, and rules for how the banks should administer loans. Also, the Act imposed a 10 percent tax on state banknotes.

More history and facts
The Federal Reserve system was established in 1913 and is run by the Federal Reserve Board in Washington, DC. The Reserve is the supreme monetary power in the United States alone and has sole power to regulate monetary policy (establishing fixed income rates, determining the supply of money, and so on) and is comprised of twelve Federal Reserve Banks located throughout USA. The number one responsibility of the Federal Reserve is to fight inflation. Each of the Federal Reserve Banks are given powers over the regular commercial and or savings banks in the district. They are the only banks allowed to put paper money (notes) in circulation, and thus makes up the entire supply of US bank notes.