Previous works concerning active galactic nuclei (AGN) variability (e.g.,Blandford \& McKee 1982) have assumed that the emission characteristics ofilluminated clouds are purely a function of the instant continuum flux to whichthey are exposed. This paper shows that this assumption is not necessarilyjustified and that the history of exposure accounting for ``local delays" dueto finite cloud equilibrium times can also be relevant. For this reason, a newformalism is developed in this paper for computing the observational propertiesof models which have local delays. The nature of the nonlinear behavior thatresults is calculated for some very simple nonlinear cloud line emissionmodels. It is found that the mean response time is a function of the recentaverage value of the continuum. Linear models fit to these nonlinear systemsrespond too slowly when there are low-energy (and generally rapid) changes inthe continuum, yet respond too rapidly when there are high-energy (andgenerally slow) changes in the continuum. As with systems without local delays,the expression for the time-dependent line flux contains an integration overhistory of the ``spatial" response function, which has structure at lags of thelight travel times of the emission region. However, the kernel of this integralitself is a function of additional integrations over individual ``cloud"response functions which have structure at lags of the equilibrium times of thecloud properties relevant to line emission. If instantaneous or linear responseis incorrectly assumed, local delays and nonlinear response can make a systemappear larger than it actually is. These effects are similar to those thatbeaming can cause. Local delays can also be a source of asymmetry about thepeak of the cross-correlation function.
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