•Friction-induced vibrations may arise in viscoelastic contacts.•Contact interactions depend on the relative speed and on the indentation depth.•Instability may occur due to negative damping terms.•In plane and out-of-plane motion are coupled through the contact interface.•Multiple stable solutions exist in certain range of system parameters. Self-excited vibrations represent a big concern in engineering, particularly in automotive, railway and aeronautic industry. Many lumped models have been proposed over the years to analyze the stability of such systems. Among the instability mechanisms a falling characteristic of the friction law and mode coupling have been shown to give friction-excited oscillations. The mass-on-moving-belt system has been studied extensively in Literature, very often adopting a prescribed form of the friction law and linearizing the contact stiffness. Instead, in this work, the case of a spherical oscillator excited by a moving viscoelastic halfspace is considered. The friction law and the nonlinear normal contact stiffness have been computed via boundary element numerical simulations for varying substrate velocity and indentation depth, then they have been adopted in time-marching dynamical numerical simulations. It is shown that the horizontal and vertical dynamics of the oscillator are tightly connected each other through the viscoelastic substrate. Furthermore, for certain normal forces/substrate velocity, the system has multiple stable solutions, which may include lift-off of the oscillator, which are selected based solely on the system initial conditions.