Two general models are proposed for the Eulerian time correlation function in homogeneous isotropic turbulence. The first is based on continued fraction approximations to its Laplace transform, and the second is based on random sweeping by a possibly non-Gaussian velocity field. Both models can give reasonable quantitative agreement with Direct Numerical Simulation (DNS) data for moderate time separations over which the time correlation functions at different wavenumbers exhibit a common self-similar form.