Interleague play in Major League Baseball refers to regular-season baseball games played between an American League (AL) team and a National League (NL) team. Interleague play was first introduced in the 1997 Major League Baseball season. Prior to that, matchups between AL teams and NL teams occurred only during spring training, the All-Star Game, other exhibition games (such as the Hall of Fame Game in Cooperstown, New York), and the World Series. Unlike modern interleague play, none of these contests, except for the World Series, counted toward official team or league records.

do american league teams play against national league teams?
yes