Two types of current instability were studied experimentally in cold-emission electron sources. Long term drifts were recorded in narrow (d = 10 – 100 mm) vacuum gaps of the sources. They are explained by adsorption-desorption processes at cathode surfaces. Fluctuations of emission currents in the sources with fresh cathodes were studied. Power spectra of current fluctuations were recorded and compared with known laws of noise spectra of emission.