The shear resistance of slipping surfaces at fixed normal stress is given by τ = τ(V, state). Here V = slip velocity, dependence on “state” is equivalent to functional dependence with fading memory on prior V(t), and ∂τ(V, state)/∂V>0. We establish linear stability conditions for steady slip states (V(t), τ(t) constant). For single degree-of-freedom elastic or viscoelastic dynamical systems, instability occurs, if at all, by a flutter mode when the spring stiffness (or appropriate viscoelastic generalization) reduces to a critical value. Similar conclusions are reached for slipping continua with spatially periodic perturbations along their interface, and in this case the existence of propagating frictional creep waves is established at critical conditions. Increases in inertia of the slipping systems are found to be destabilizing, in that they increase the critical stiffness level required for stability.