We propose a family of two-dimensional incopressible fluid models indexed by a parameter alpha, ranging from 0 to infinity, and discuss the spectral scaling properties for homogeneous, isotropic turbulence in these models. The family includes two physically realizable members. It is shown that the enstrophy cascade is spectrally local for alpha less than 2, but becomes dominated by nonlocal interactions for alpha greater than 2. Numerical simulations indicate that the spectral slopes are systematically steeper than those predicted by the local scaling argument.