Carbon exchange by the terrestrial biosphere is thought to have changed since pre-industrial times in response to increasing concentrations of atmospheric CO2 and variations (anomalies) in inter-annual air temperatures. However, the magnitude of this response, particularly that of various ecosystem types (biomes), is uncertain. Terrestrial carbon models can be used to estimate the direction and size of the terrestrial responses expected, providing that these models have a reasonable theoretical base. We formulated a general model of ecosystem carbon fluxes by linking a process-based canopy photosynthesis model to the Rothamsted soil carbon model for biomes that are not significantly affected by water limitation. The difference between net primary production (NPP) and heterotrophic soil respiration (Rh) represents net ecosystem production (NEP). The model includes (i) multiple compartments for carbon storage in vegetation and soil organic matter, (ii) the effects of seasonal changes in environmental parameters on annual NEP, and (iii) the effects of inter-annual temperature variations on annual NEP. Past, present and projected changes in atmospheric CO2 concentration and surface air temperature (at different latitudes) were analysed for their effects on annual NEP in tundra, boreal forest and humid tropical forest biomes. In all three biomes, annual NEP was predicted to increase with CO2 concentration but to decrease with warming. As CO2 concentrations and temperatures rise, the positive carbon gains through increased NPP are often outweighed by losses through increased Rh, particularly at high latitudes where global warming has been (and is expected to be) most severe. We calculated that, several times during the past 140 years, both the tundra and boreal forest biomes have switched between being carbon sources (annual NEP negative) and being carbon sinks (annual NEP positive). Most recently, significant warming at high latitudes during 1988 and 1990 caused the tundra and boreal forests to be net carbon sources. Humid tropical forests generally have been a carbon sink since 1960. These modelled responses of the various biomes are in agreement with other estimates from either field measurements or geochemical models. Under projected CO2 and temperature increases, the tundra and boreal forests will emit increasingly more carbon to the atmosphere while the humid tropical forest will continue to store carbon. Our analyses also indicate that the relative increase in the seasonal amplitude of the accumulated NEP within a year is about 0–14% year−1 for boreal forests and 0–23% year−1 in the tundra between 1960 and 1990.