The chapter discusses the stability of steady frictional slipping in mechanical systems. It begins by introducing the concept of steady sliding and its stability, highlighting the contradiction between classical stability analysis and experimental observations. The chapter then presents a constitutive framework for frictional slip, where the shear stress $\tau$ depends on both the slip rate $V$ and the state of the surface, which evolves with ongoing slip. This framework is used to derive linear stability conditions for steady-slip states. For single-degree-of-freedom elastic or viscoelastic systems, instability occurs through a flutter mode when the spring stiffness (or viscoelastic generalization) reaches a critical value. Similar conclusions are drawn for slipping continua with spatially periodic perturbations, where the existence of propagating frictional creep waves is established at critical conditions. The inclusion of inertia in the system is found to be destabilizing, increasing the critical stiffness required for stability. The chapter also explores the stability of one-degree-of-freedom elastic systems, showing that as the stiffness decreases from infinity to zero, a critical value is reached where the system transitions from stable to unstable. The critical frequency and stiffness are derived, and the conditions for instability are discussed. The analysis is extended to viscoelastic systems, where the critical conditions for instability are similar but involve additional terms related to the viscoelastic relaxation function. Finally, the chapter discusses the stability of slipping elastic continua and the effects of inertia in antiplane perturbations. It shows that the critical wave number for instability depends on the elastic properties of the materials and the frictional law. The analysis predicts that disturbances with wavelengths shorter than a critical wavelength decay, while those longer exhibit oscillatory growth. The concluding discussion emphasizes the universality of the flutter instability pattern and the importance of rate and state-dependent frictional constitutive laws in understanding the nonlinear behavior of such systems.The chapter discusses the stability of steady frictional slipping in mechanical systems. It begins by introducing the concept of steady sliding and its stability, highlighting the contradiction between classical stability analysis and experimental observations. The chapter then presents a constitutive framework for frictional slip, where the shear stress $\tau$ depends on both the slip rate $V$ and the state of the surface, which evolves with ongoing slip. This framework is used to derive linear stability conditions for steady-slip states. For single-degree-of-freedom elastic or viscoelastic systems, instability occurs through a flutter mode when the spring stiffness (or viscoelastic generalization) reaches a critical value. Similar conclusions are drawn for slipping continua with spatially periodic perturbations, where the existence of propagating frictional creep waves is established at critical conditions. The inclusion of inertia in the system is found to be destabilizing, increasing the critical stiffness required for stability. The chapter also explores the stability of one-degree-of-freedom elastic systems, showing that as the stiffness decreases from infinity to zero, a critical value is reached where the system transitions from stable to unstable. The critical frequency and stiffness are derived, and the conditions for instability are discussed. The analysis is extended to viscoelastic systems, where the critical conditions for instability are similar but involve additional terms related to the viscoelastic relaxation function. Finally, the chapter discusses the stability of slipping elastic continua and the effects of inertia in antiplane perturbations. It shows that the critical wave number for instability depends on the elastic properties of the materials and the frictional law. The analysis predicts that disturbances with wavelengths shorter than a critical wavelength decay, while those longer exhibit oscillatory growth. The concluding discussion emphasizes the universality of the flutter instability pattern and the importance of rate and state-dependent frictional constitutive laws in understanding the nonlinear behavior of such systems.