Valence- and conduction-band densities of states of GexSe1-x thin films (0 less than or equal to x less than or equal to 0.333) were investigated by measuring ultraviolet photoemission and inverse-photoemission spectra. They exhibit remarkable changes in their spectral features near x = 0.20 from amorphous Se-like to amorphous GeSe2-like. These observations in the electronic structures are consistent with the occurrence of a percolation threshold in non-crystalline covalent network systems as predicted by Phillips and Thorpe.