Dieterich, J.H., 1992. Earthquake nucleation on faults with rate- and state-dependent strength. In: T. Mikumo, K. Aki, M. Ohnaka, L.J. Ruff and P.K.P. Spudich (Editors), Earthquake Source Physics and Earthquake Precursors. Tectonophysics, 211: 115-134. Faults with rate- and state-dependent constitutive properties reproduce a range of observed fault slip phenomena including spontaneous nucleation of slip instabilities at stresses above some critical stress level and recovery of strength following slip instability. Calculations with a plane-strain fault model with spatially varying properties demonstrate that accelerating slip precedes instability and becomes localized to a fault patch. The dimensions of the fault patch follow scaling relations for the minimum critical length for unstable fault slip. The critical length is a function of normal stress, loading conditions and constitutive parameters which include Dc, the characteristic slip distance. If slip starts on a patch that exceeds the critical size, the length of the rapidly accelerating zone tends to shrink to the characteristic size as the time of instability approaches. Solutions have been obtained for a uniform, fixed-patch model that are in good agreement with results from the plane-strain model. Over a wide range of conditions, above the steady-state stress, the logarithm of the time to instability linearly decreases as the initial stress increases. Because nucleation patch length and premonitory displacement are proportional to Dc, the moment of premonitory slip scales by D3c. The scaling of Dc is currently an open question. Unless Dc for earthquake faults is significantly greater than that observed on laboratory faults, premonitory strain arising from the nucleation process for earthquakes may by too small to detect using current observation methods. Excluding the possibility that Dc in the nucleation zone controls the magnitude of the subsequent earthquake, then the source dimensions of the smallest earthquakes in a region provide an upper limit for the size of the nucleation patch. ?? 1992.