An oscillator system (30) of a mechanical timepiece, comprising: at least one balance wheel (35) that is free to rotate about an axis; and at least one hairspring (31) connecting the at least one balance wheel (35) to a fixed point or to another balance wheel (36), the hairspring (31) including: a first coil (32) connected to the at least one balance wheel (35); and a second coil (33) connected to the fixed point or to the another balance wheel (36); and a transition section (34) connecting the first coil (32) to the second coil (33), wherein an approximately linear restoring torque for the at least one balance wheel (35) is primarily provided by elastic deformation of the transition section (34) and the coils (32, 33), in order to generate an oscillatory motion for the at least one balance wheel (35).