Atmospheric changes that may affect physiological and biogeochemical processes in old–growth tropical forests include: (i) rising atmospheric CO2 concentration; (ii) an increase in land surface temperature; (iii) changes in precipitation and ecosystem moisture status; and (iv) altered disturbance regimes. Elevated CO2 is likely to directly influence numerous leaf–level physiological processes, but whether these changes are ultimately reflected in altered ecosystem carbon storage is unclear. The net primary productivity (NPP) response of old–growth tropical forests to elevated CO2 is unknown, but unlikely to exceed the maximum experimentally measured 25% increase in NPP with a doubling of atmospheric CO2 from pre–industrial levels. In addition, evolutionary constraints exhibited by tropical plants adapted to low CO2 levels during most of the Late Pleistocene, may result in little response to increased carbon availability. To set a maximum potential response for a Central Amazon forest, using an individual–tree–based carbon cycling model, a modelling experiment was performed constituting a 25% increase in tree growth rate, linked to the known and expected increase in atmospheric CO2. Results demonstrated a maximum carbon sequestration rate of ca. 0.2 Mg C per hectare per year (ha−1 yr−1, where 1 ha = 104 m2), and a sequestration rate of only 0.05 Mg C ha−1 yr−1 for an interval centred on calendar years 1980–2020. This low rate results from slow growing trees and the long residence time of carbon in woody tissues. By contrast, changes in disturbance frequency, precipitation patterns and other environmental factors can cause marked and relatively rapid shifts in ecosystem carbon storage. It is our view that observed changes in tropical forest inventory plots over the past few decades is more probably being driven by changes in disturbance or other environmental factors, than by a response to elevated CO2. Whether these observed changes in tropical forests are the beginning of long–term permanent shifts or a transient response is uncertain and remains an important research priority.