The observational predictions of various nonstandard cosmological models which have an FRW metric as their space-time geometry are investigated. The general numerical predictions of the models are found to be in accord with actual observations; in particular, they predict a current relative velocity of the Galaxy with respect to the CMB consistent with measurements of the dipole anisotropy of the CMB temperature distribution, and also predict a quadrupole anisotropy, the magnitude of which is well below the upper limits obtained from observations. The distance versus redshift relationship is calculated in a typical model and is found to be the same as in the corresponding standard FRW model. The critical density problem is addressed, and the behavior of the expansion in the models is investigated. The thermodynamics of the models is considered, and the predicted helium abundance in the models is calculated and found to be in accord with current estimates. In particular, in a class of two-fluid models the predicted helium abundance is virtually the same as that in the corresponding standard FRW model. 31 references.