An earthquake is commonly described as a stick-slip frictional instability occurring along preexisting crustal faults. The seismic cycle of earthquake recurrence is characterised by long periods of quasi-static evolution which precede sudden slip events accompanied by elastic wave radiation: the earthquake. This succession of processes over two well distinguished time scales recalls the behaviour of nonlinear relaxation oscillations. We explore this connection by studying, in the framework of

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... te-and-state friction, the sliding of two identical slabs of elastic solid driven in opposite directions with a constant relative velocity. Our first innovation is to establish that the motion of a spring-block system is an asymptotic mechanical analogue of the frictional sliding of a single interface from which elastic waves radiate. Due to wave reflection at the boundaries, the equivalent mass of the block M = k(h/cs) 2 /12 is not independent of the equivalent spring stiffness k, where h denotes the slab thickness and cs is the shear wave speed. Considering a non-monotonic friction law, we show that the relaxation oscillation regime is reached when the characteristic time scale of frictionless oscillations is much greater than the characteristic time of frictional memory effects: (M/k) 1/2 L/V * . We combine a composite approximation of the stick-slip cycle and numerical studies to show that the interfacial relaxation oscillations result from the subtle interplay of the non-monotonic properties of the friction law driving the long stress build-up of the quasi-static phase, and the inertial control of the fast slip phase originating from the wave propagation. We discuss the geophysical consequences for earthquake mechanics, and connections between the rate-and-state and Coulomb models of friction.