There are 2 train companies operating 4 routes - ICE82, RE11, SE10, RE1. The cheapest train costs $38 and is 3h 28min.
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There are 4 ways to travel from FRA to LUX. 1 flight, 3 trains, 4 buses and 1 by car are possible between the two areas. The by car from FRA to LUX is the cheapest. The by car from FRA to LUX is the fastest. The train operated by running from Kelsterbach to Saarburg is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!