A system having vehicles, each including a secondary coil for the inductive supply of the vehicle from a primary conductor system, wherein the secondary coil includes a coil core, which has at least one main limb, the secondary coil being made up of a first and a second coil, each composed of windings which enclose the main limb in each case, the first coil arranged such that the windings are connected in series, and the induction voltage arising at the coil corresponds to the sum of the individual voltages induced at all windings when the magnetic flux enclosed by an individual winding in the main limb always has the same direction, especially in each winding of the first coil, the second coil arranged such that the second coil is made up of a first type of windings, i.e., a first partial coil, and of a second type of windings.