Exponential spatial growth of electron swarms in gases under steady-state Townsend conditions may be observed not only in the downstream region of an electron source but also in the upstream region due to backward diffusion. Relations among swarm parameters in the upstream region were deduced and found to have peculiar characteristics. For example, the sign of the average electron velocity vd for steadystate Townsend conditions depends on whether the gas is electro-positive or electronegative. This property is confirmed quantitatively by calculating the electron energy distribution using a propagator method modified for analysis in the upstream region. As an example of the effect of backward diffusion, the decay in the electron number density in front of the anode in a steady-state Townsend experiment between parallel plane electrodes was studied. The decay is caused by the missing electrons absorbed at the anode. The energy distribution of the missing electrons has a non-equilibrium relaxation region and the equilibrium region lies towards the cathode direction. The number density of the missing electrons showed an exponential spatial dependence in the equilibrium region. The relative gradient of the decrease agreed well with the relative density gradient ? obtained in the upstream region. It was also found that the electron energy distribution in the decaying region tends to that in the upstream equilibrium region.