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This paper deals with potential nonlinear effects in nucleate boiling systems as a result of the behavior of individual nucleation sites on the heater surface. This requires detailed microscopic modeling of the surface. A computational model has been formulated for this purpose. The model addresses the three-dimensional transient conduction heat transfer process within the problem domain comprised of the macrolayer and heater. Hydrodynamic effects are represented through boundary conditions. Individual nucleation sites are activated or deactivated depending on the thermal conditions that prevail at the site. The model has been used to examine the behavior of sites on a realistic heater surface. The results indicate that significant spatial and temporal temperature variations can occur on the surface, and that thermal interactions among sites can result in some sites operating intermittently. Surface-averaged temperatures show nonlinear period-doubling behavior. A chaotic case was found. Qualitative comparisons are made to both local instantaneous temperature measurements and recent experiments that showed chaotic behavior. We believe that such nonlinear behavior is one of the reasons that mechanistic predictive capabilities for the boiling process have remained elusive.