A brushless electrical machine, in particular, a brushless d.c. motor, having a housing, at least one rotor, which is positioned on a shaft rotationally mounted in the housing, and a stator attached to the housing; the rotor being assigned a rotor position detection device, which operates contactlessly and includes a multipole magnetic ring positioned on the shaft in a rotatably fixed manner and at least one sensor, which is sensitive to magnetic fields and is attached to the housing radially with respect to the outer circumference of the magnetic ring. The number of pole pairs of the rotor and the number of pole pairs of the magnetic ring are coprime.