Magnitudes and redshifts of quasi-stellar objects measured by L,ynds, by Sandage, and by Schmidt are discussed on the supposition that the objects are "cosmological' sources in a model universe. The inferred intrinsic properties of the radiation emitted by the sources are considered; while the properties show considerable dispersion, they confirm that we are treating a single category. This appears to be characterized by a very flat spectrum to which a good approximation is given by a formula used by Sandage; an attempt is made to synthesize a spectrum over the range about 6 to 26 X 1014 c/s. Evidence is encountered for distinguishing some five of the sources as a possibly significant subset. Schmidt's concept of estimating the emitted flux at a particular emitted frequency is exploited; when this flux is plotted against redshift, the diagram is compatible with the existence of an envelope for brightest sources, and this may assist in discriminating between models. The absence of points in part of this and other diagrams is accounted for by the fact that the optical observations do not yet include sources with apparent magnitude fainter than about 18. Another instructive diagram shows the results of calculating how the observed sources would appear were they transferred to other distances in the model. The discussion is illustrated for three particular cosmological models: the special-relativity model, the steadystate model, an evolutionary model used by Schmidt. The observations are not indisputably incompatible with any of these. General considerations and minor features make the last model possibly the least plausible. General considerations make the steady-state model plausible, but special features appear possibly unfavorable. The special-relativity model represents the observations quite plausibly. But this case can be regarded either as a particular cosmological model or as a description of a cosmically local phenomenon. It may be necessary to contemplate the possibility that the sources are not "cosmological."