The invention relates to a system (1) for transporting round hay bales (2), which includes a means of (3) of traction for said round hay bales (2) and a means (4) of pulling said means (3) of traction for moving said round bales (2) in a transport direction, and is characterized in that said means (3) of traction are mounted so that they rotate around a longitudinal shaft ("Y") of said pulling means, said means (3) of traction being able to rotate freely around said shaft ("Y") to allow the round bales (2) to move relative to said pulling means (4). The system prevents the baling ties from breaking, allows auto-alignment of the round bales and gives the round bales very small turning radii.