The global atmospheric methane burden has more than doubled since pre-industrial times,, and this increase is responsible for about 20% of the estimated change in direct radiative forcing due to anthropogenic greenhouse-gas emissions. Research into future climate change and the development of remedial environmental policies therefore require a reliable assessment of the long-term growth rate in the atmospheric methane load. Measurements have revealed that although the global atmospheric methane burden continues to increase with significant interannual variability,, the overall rate of increase has slowed,. Here we present an analysis of methane measurements from a global air sampling network that suggests that, assuming constant OH concentration, global annual methane emissions have remained nearly constant during the period 1984-96, and that the decreasing growth rate in atmospheric methane reflects the approach to a steady state on a timescale comparable to methane's atmospheric lifetime. If the global methane sources and OH concentration continue to remain constant, we expect average methane mixing ratios to increase slowly from today's 1,730nmolmol-1 to ~1,800nmolmol-1, with little change in the contribution of methane to the greenhouse effect.