The invention relates to the alfalfa variety designated RRL43A108. Provided bytheinvention are the seeds, plants and derivatives of the alfalfa varietyRRL43A108. Alsoprovided by the invention are tissue cultures of the alfalfa variety RRL43A108and the plantsregenerated therefrom. Still further provided by the invention are methods forproducingalfalfa plants by crossing the alfalfa variety RRL43A108 with itself oranother alfalfa varietyand plants produced by such methods.