We prepared concentrated quasi monodisperse hexadecane-in-water emulsions stabilized by various proteins and investigated their rheological properties. Some protein-stabilized emulsions possess remarkably high elasticity and at the same time they are considerably fragile--they exhibit coalescence at yield strain and practically do not flow. The elastic storage modulus G' and the loss modulus G" of the emulsions were determined for different oil volume fractions above the random close packing. Surprisingly, the dimensionless elastic moduli G'/(sigma/a), sigma being the interfacial tension, and a being the mean drop radius, obtained for emulsions stabilized by different proteins do not collapse on a single master curve. They are almost always substantially higher than the corresponding values obtained for equivalent Sodium Dodecyl Sulfate (SDS)-stabilized emulsions. The unusually high elasticity cannot be attributed to a specificity of the continuous phase, because the osmotic equation of state of our emulsions is found identical to the one obtained for samples stabilized by classical surfactants. In parallel, we mimicked the thin films that separate the droplets in the concentrated emulsion and found that the protein adsorption layers contain a substantial number of sticky surface aggregates. These severely obstruct local rearrangements of individual drops in respect to their neighbors which leads to coalescence at yield strain. Furthermore, we found that G'/(sigma/a) is correlated (for a given oil volume fraction) to the dilatational elastic modulus, of the protein layer adsorbed on the droplets. The intrinsic elasticity of the protein layers, together with the blocked local rearrangements are considered as the main factors determining the unusual bulk elasticity of the studied emulsions.