Theoretical prejudice and inflationary models of the very early Universe strongly favor the flat, Einstein-deSitter model of the Universe. At present the observational data conflict with this prejudice. This conflict can be resolved by considering flat models of the Universe which possess a smooth component by energy density. We study in detail the kinematics of such models, where the smooth component is relativistic particles, a cosmological term, a network of light strings, or fast-moving, light strings. We also discuss the observational tests which can be used to discriminate between these models. These tests include the magnitude-redshift, lookback time-redshift, angular size-redshift, and comoving volume-redshift diagrams and the growth of density fluctuations.