We test cosmological models with ΩE1 using the COBE two-year cross-correlation function by means of a maximum-likelihood test with Monte Carlo realizations of several Ω models. Assuming a Harrison-Zel8dovich primordial power spectrum with amplitude PQ, it is found that there is a large region in the (Ω, Q), parameter space that fits the data equally well. We find that the flatness of the universe is not implied by the data. A summary of other analyses of COBE data to constrain the shape of the primordial spectrum is presented.