In the first part, we investigate uncertainties inherent in the observational determinations of virial masses for groups of galaxies. This is done by computing virial theorem masses of small N-body configurations for three different ensembles representing groups of 8, 16, or 32 galaxies. Dynamical evolution, projection effects, and the effects of incomplete data are used to simulate actual observations. Instantaneous departures from equilibrium and projection effects introduce an uncertainty of about 50 percent in the computed masses. Selection of heavy (and presumably more luminous) members usually produces a significant underestimate of both the actual and projected virial masses of bound clusters. The validity of theoretical assumptions is tested against dynamically consistent configurations of one N-body system with 500 particles. The virial mass derived from cylindrical samples of centrally condensed models also underestimates the actual mass, even though the selected velocities exceed the rms value. The average net result of these effects is to increase the discrepancy between virial and luminosity masses for groups and clusters. In the second part, we examine the observational implications of the hypothesis that groups of galaxies are unbound and expanding. Detailed models of initial instability or significant mass loss are considered. Groups with positive energy expand rapidly, and the apparent mass discrepancy based on the equilibrium assumption is magnified by the linear growth factor as well as the initial excess. Evolution tracks of virial masses have also been computed for several types of mass-loss mechanisms and different rates. A range of mass discrepancies consistent with observations can easily be reproduced from relatively moderate assumptions. Finally, we discuss several methods for distinguishing between the hidden-mass hypothesis and the expansion hypothesis.