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After som searching I found a movie that contain one 1957 Chevy and also a Mustang and a Chevelle that looks to be racing. So I guess it must be the 1989 movie "Catch Me If You Can":
http://imcdb.org/movie_97029-Catch-Me-If-You-Can.html
http://imcdb.org/movie_97029-Catch-Me-If-You-Can.html