The question of the "glassiness" of hydrated protein systems is examined by comparing reported observations on proteins with the characteristic features, both long time and very short time aspects, of the liquid-to-glass transition in liquid and polymer systems. In an attempt to reconcile conflicting features, the calorimetric behavior of the much-studied hydrophilic proteins, myoglobin and cytochrome c, has been determined by differential scanning calorimetry and compared with that of a model system, the hydrated monopeptide poly-L-asparagine of comparable molecular weight. The results are analyzed in terms of the three canonical features of relaxation in glass-forming systems : non-Arrhenius character (fragility), nonexponentiality, and nonlinearity. The homopeptide has a nonfreezing water range comparable to the ice-saturated proteins, both native and denatured. Studies of the scan rate dependence of T-g for a range of water contents from 14 to 29 wt % imply that the hydrated homopeptide system behaves as a "strong" liquid at all water contents. We show that this is consistent with the behavior of native proteins according to earlier studies. However, anneal and scan studies, particularly on hydrated cytochrome c, confirm the existence of an extremely broad distribution of relaxation times in the proteins. From these observations, and from comparison with data on related systems, we conclude that hydrated proteins indeed may be classed among glass-forming systems, but due to their special structural features and to the disposition of the bound water, they show great departures from thermorheological simplicity. This seems to be partly a consequence of a special strengthening, in fully hydrated proteins, of the secondary (beta) relaxations which are not calorically important in most glass-forming systems. We suggest that this may have developed to take advantage of the fast side chain dynamics typical of polymer systems and thereby to reduce the ambient temperature response times of biologically important processes. In the solution systems of this study, this feature smears out the glass transition almost beyond recognition. An analogy between the weakly first-order strong-to-fragile liquid transition in low-temperature water and the denaturing transition in proteins is briefly discussed.