1. An electronic endoscope apparatus comprising: a light source for illuminating an interior portion of a biological body under medical examination; filter means selectively interposed between the light source and illuminated interior portion of the biological body for filtering out light having a preselected transmission wavelength, and for projecting said filtered light to the interior portion thereof; image sensor means for imaging the illuminated interior portion by receiving the filtered light therefrom to thereby produce a functional information image signal; means for processing said functional information image signal so as to detect a region having an exposure level exceeding over an allowable maximum exposure level, and for superimposing said region having the over-exposure level on said functional information image signal; and means for displaying both a functional information image of the biological body and said over-exposure region superimposed thereon based upon said functional information image signal and said over-exposure region.