[1] Previous studies have found that earthquake nucleation on faults with rate-and-state dependent constitutive properties is a time dependent process involving evolution of slip rate v and frictional state variable θ. The evolution of θ is governed by an extended aging law, which accounts for the effects of normal stress variations. Assuming normal stress along the fault varies due to remote stressing, we derive a generalized simple patch (GSP) solution that explicitly describes quasi-static evolution of v and θ in the aseismic period, which is shown to agree well with simulation results from a 2D plane strain model. The GSP solution suggests that both initial and loading conditions affect time to instability ti. For initial conditions satisfying Ω = vθ/Dc > 1, ti is strongly dependent on initial slip rate but is insensitive to remote stressing rate. For Ω ≤ 1, ti is affected by initial slip rate, initial state variable and remote loading rate (both shear and normal). Using the GSP solution, we calculate aftershock rates following a Coulomb stress step, which generally agree with Omori's decay law. Our results show that nucleation process is strongly affected by normal stress variations purely originated from remote stressing, which implies that nucleation process on nonplanar faults may be quite different from those observed from planar fault models with pure shear loading conditions, since normal stress variations can arise due to both fault slip and remote stressing for nonplanar faults.