Lateral electric conductivity of mica-supported lipid monolayers and of the corresponding lipid bilayers has been studied by means of scanning tunneling microscopy (STM). The surface of freshly cleaved mica itself was found to be conductive when exposed to humid air. Lipid monolayers were transferred onto such a surface by means of the Langmuir-Blodgett technique, which makes the mica surface hydrophobic and suppresses the electric current along the surface in the experimentally accessible humidity (5-80%) and applied voltage (0-10 V) range. This is true for dipalmitoylphosphatidylethanolamine (DPPE) as well as dipalmitoylphosphatidylcholine (DPPC) monolayers. Repeated deposition of DPPC layers by means of the Langmuir-Blodgett LB technique does not lead to the formation of a stable surface-supported bilayer because of the high hydrophilicity of the phosphatidylcholine headgroups that causes DPPC/DPPC bilayers to peel off the supporting surface during the sample preparation. In contrast to this, a DPPE or a DPPC monolayer on top of a DPPE monolayer gives rise to a rather stable mica-supported bilayer that can be studied by STM. Electric currents between 10 and 100 fA, depending on the ambient humidity, flow along the DPPE bilayer surface, in the humidity range between 35 and 60%. The DPPC surface, which is more hydrophilic, is up to 100 times more conductive under comparable conditions. Anomalous high lateral conductivity thus depends on, and probably proceeds via, the surface-adsorbed water layers. The prominence of ambient humidity and surface hydrophilicity on the measured lateral currents suggests this. The combination of our STM data and previously published water adsorption isotherms as a function of the relative humidity indicate that one layer or less of adsorbed water suffices for mediating the measurable lateral currents. The fact that similar observations are also made for other hydrophilic substrates supports the conclusion that lateral conductivity via surface-adsorbed water is a rather general phenomenon.