Quite a few different kinds of spaces like 1-st countable spaces, sequential spaces and M-spaces have been characterized as images or inverse images of metric spaces by unique-valued mappings satisfying certain conditions, but so far little efforts have been made to take advantage of multi-valued mappings in this aspect of study. The purpose of the present paper is to show usefulness of such mappings in characterization of two interesting classes of generalized metric spaces, a-spaces (due to [4] ) and M*-spaces (due to [2] ).