Abstract Parametric resonances are studied which occur when an elastic system is rotated around an annular disc with friction having a negative slope with velocity. The elastic system consists of two spring–dashpots, in the transverse and in-plane (circumferential) directions, and a common point mass. The complete arrangement is driven around the disc through the in-plane stiffness and damper. It is demonstrated that the effect of the in-plane system (including the negative friction–velocity relationship) is (i) to introduce additional parametric resonances which are destabilised by the transverse damper, and (ii) to reduce the regions of instability of the other resonances.