Observational evidence for both static and transient nearâfield and farâfield triggered seismicity are explained in terms of a frictional instability model, based on a single degree of freedom springâslider system and rateâ and stateâdependent frictional constitutive equations. In this study a triggered earthquake is one whose failure time has been advanced by Ît (clock advance) due to a stress perturbation. Triggering stress perturbations considered include squareâwave transients and step functions, analogous to seismic waves and coseismic static stress changes, respectively. Perturbations are superimposed on a constant background stressing rate which represents the tectonic stressing rate. The normal stress is assumed to be constant. Approximate, closedâform solutions of the rateâandâstate equations are derived for these triggering and background loads, building on the work of Dieterich [1992, 1994]. These solutions can be used to simulate the effects of static and transient stresses as a function of amplitude, onset time t0, and in the case of square waves, duration. The accuracies of the approximate closedâform solutions are also evaluated with respect to the full numerical solution and t0. The approximate solutions underpredict the full solutions, although the difference decreases as t0 approaches the end of the earthquake cycle. The relationship between Ît and t0 differs for transient and static loads: a static stress step imposed late in the cycle causes less clock advance than an equal step imposed earlier, whereas a later applied transient causes greater clock advance than an equal one imposed earlier. For equal Ît, transient amplitudes must be greater than static loads by factors of several tens to hundreds depending on t0. We show that the rateâandâstate model requires that the total slip at failure is a constant, regardless of the loading history. Thus a static load applied early in the cycle, or a transient applied at any time, reduces the stress at the initiation of failure, whereas static loads that are applied sufficiently late raise it. Rateâandâstate friction predictions differ markedly from those based on Coulomb failure stress changes (ÎCFS) in which Ît equals the amplitude of the static stress change divided by the background stressing rate. The ÎCFS model assumes a stress failure threshold, while the rateâandâstate equations require a slip failure threshold. The complete rateâandâstate equations predict larger Ît than the ÎCFS model does for static stress steps at small t0, and smaller Ît than the ÎCFS model for stress steps at large t0. The ÎCFS model predicts nonzero Ît only for transient loads that raise the stress to failure stress levels during the transient. In contrast, the rateâandâstate model predicts nonzero Ît for smaller loads, and triggered failure may occur well after the transient is finished. We consider heuristically the effects of triggering on a population of faults, as these effects might be evident in seismicity data. Triggering is manifest as an initial increase in seismicity rate that may be followed by a quiescence or by a return to the background rate. Available seismicity data are insufficient to discriminate whether triggered earthquakes are ânewâ or clock advanced. However, if triggering indeed results from advancing the failure time of inevitable earthquakes, then our modeling suggests that a quiescence always follows transient triggering and that the duration of increased seismicity also cannot exceed the duration of a triggering transient load. Quiescence follows static triggering only if the population of available faults is finite.